@article{misra_stitzinger_yu_2021, title={Subinvariance in Leibniz algebras}, volume={567}, ISSN={["1090-266X"]}, url={https://doi.org/10.1016/j.jalgebra.2020.09.031}, DOI={10.1016/j.jalgebra.2020.09.031}, abstractNote={Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant subalgebras of Leibniz algebras and study their properties. It is shown that the signature results on subinvariance in Lie algebras have analogs for Leibniz algebras.}, journal={JOURNAL OF ALGEBRA}, publisher={Elsevier BV}, author={Misra, Kailash C. and Stitzinger, Ernie and Yu, Xingjian}, year={2021}, month={Feb}, pages={128–138} }
@article{boyle_misra_stitzinger_2020, title={Complete Leibniz algebras}, volume={557}, ISSN={["1090-266X"]}, url={https://doi.org/10.1016/j.jalgebra.2020.04.016}, DOI={10.1016/j.jalgebra.2020.04.016}, abstractNote={Leibniz algebras are certain generalizations of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of complete Leibniz algebras as a generalization of complete Lie algebras. Then we study properties of complete Leibniz algebras and their holomorphs.}, journal={JOURNAL OF ALGEBRA}, publisher={Elsevier BV}, author={Boyle, Kristen and Misra, Kailash C. and Stitzinger, Ernest}, year={2020}, month={Sep}, pages={172–180} }
@article{mcalister_rovira_stitzinger_2019, title={FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS}, volume={25}, DOI={10.24330/ieja.504114}, abstractNote={Ideals that share properties with the Frattini ideal of a Leibniz algebra are studied. Similar investigations have been considered in group the- ory. The results will hold for Lie algebras as well. Many of the results involve nilpotency of these algebras.}, journal={INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA}, author={McAlister, Allison and Rovira, Kristen Stagg and Stitzinger, Ernest}, year={2019}, pages={64–76} }
@article{stitzinger_white_2018, title={Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras}, volume={21}, ISSN={["1572-9079"]}, DOI={10.1007/s10468-017-9731-y}, abstractNote={We extend conjugacy results from Lie algebras to their Leibniz algebra generalizations. The proofs in the Lie case depend on anti-commutativity. Thus it is necessary to find other paths in the Leibniz case. Some of these results involve Cartan subalgebras. Our results can be used to extend other results on Cartan subalgebras. We show an example here and others will be shown in future work.}, number={3}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Stitzinger, Ernie and White, Ashley}, year={2018}, month={Jun}, pages={627–633} }
@article{misra_stitzinger_turner_2018, title={Criteria for solvability and supersolvability in Leibniz algebras}, volume={46}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2017.1372455}, abstractNote={Leibniz algebras are certain generalization of Lie algebras. Recently, analyzing the structure of subalgebras, David Towers gave some criteria for the solvability and supersolvability of Lie algebras. In this paper we define analogues concepts for Leibniz algebras and extend some of these results on solvability and supersolvability to that of Leibniz algebras.}, number={5}, journal={COMMUNICATIONS IN ALGEBRA}, author={Misra, Kailash C. and Stitzinger, Ernie and Turner, Bethany}, year={2018}, pages={2083–2088} }
@article{demir_misra_stitzinger_2017, title={On classification of four-dimensional nilpotent Leibniz algebras}, volume={45}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2016.1172626}, abstractNote={Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.}, number={3}, journal={COMMUNICATIONS IN ALGEBRA}, author={Demir, Ismail and Misra, Kailash C. and Stitzinger, Ernie}, year={2017}, pages={1012–1018} }
@book{klima_sigman_stitzinger_2016, title={Applied Abstract Algebra}, ISBN={9781482248234}, publisher={Boca Raton: CRC Press}, author={Klima, R. and Sigman, N. and Stitzinger, E.}, year={2016} }
@article{demir_misra_stitzinger_2016, title={Classification of Some Solvable Leibniz Algebras}, volume={19}, ISSN={["1572-9079"]}, DOI={10.1007/s10468-015-9580-5}, abstractNote={Leibniz algebras are certain generalization of Lie algebras. In this paper we give classification of non-Lie solvable (left) Leibniz algebras of dimension ≤ 8 with one dimensional derived subalgebra. We use the canonical forms for the congruence classes of matrices of bilinear forms to obtain our result. Our approach can easily be extended to classify these algebras of higher dimensions. We also revisit the classification of three dimensional non-Lie solvable (left) Leibniz algebras.}, number={2}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Demir, Ismail and Misra, Kailash C. and Stitzinger, Ernie}, year={2016}, month={Apr}, pages={405–417} }
@article{burch_stitzinger_2016, title={TRIANGULABLE LEIBNIZ ALGEBRAS}, volume={44}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2015.1085997}, abstractNote={A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizable; that is, if all 2-generated subalgebras are triangulable, then the algebra is also. Triangulability joins solvability, supersolvability, strong solvability, and nilpotentcy as a 2-recognizable property for classes of Leibniz algebras.}, number={8}, journal={COMMUNICATIONS IN ALGEBRA}, author={Burch, Tiffany and Stitzinger, Ernie}, year={2016}, pages={3622–3625} }
@article{burch_harris_mcalister_rogers_stitzinger_sullivan_2015, title={2-recognizeable classes of Leibniz algebras}, volume={423}, ISSN={["1090-266X"]}, DOI={10.1016/j.jalgebra.2014.10.039}, abstractNote={We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and supersolvable. These same results hold in Lie algebras and in general for groups.}, journal={JOURNAL OF ALGEBRA}, author={Burch, Tiffany and Harris, Meredith and McAlister, Allison and Rogers, Elyse and Stitzinger, Ernie and Sullivan, S. McKay}, year={2015}, month={Feb}, pages={506–513} }
@article{khuhirun_misra_stitzinger_2015, title={On nilpotent Lie algebras of small breadth}, volume={444}, ISSN={["1090-266X"]}, DOI={10.1016/j.jalgebra.2015.07.036}, abstractNote={A Lie algebra L is said to be of breadth k if the maximal dimension of the images of left multiplication by elements of the algebra is k. In this paper we give characterization of finite dimensional nilpotent Lie algebras of breadth less than or equal to two. Furthermore, using these characterizations we determined the isomorphism classes of these algebras.}, journal={JOURNAL OF ALGEBRA}, author={Khuhirun, Borworn and Misra, Kailash C. and Stitzinger, Ernie}, year={2015}, month={Dec}, pages={328–338} }
@article{ray_hedges_stitzinger_2014, title={Classifying Several Classes of Leibniz Algebras}, volume={17}, ISSN={["1572-9079"]}, DOI={10.1007/s10468-013-9416-0}, abstractNote={We extend results related to maximal subalgebras and ideals from Lie to Leibniz algebras. In particular, we classify minimal non-elementary Leibniz algebras and Leibniz algebras with a unique maximal ideal. In both cases, there are types of these algebras with no Lie algebra analogue. We also give a classification of E-Leibniz algebras which is very similiar to its Lie algebra counterpart. Note that a classification of elementary Leibniz algebras has been shown in Batten Ray et al. (2011).}, number={2}, journal={ALGEBRAS AND REPRESENTATION THEORY}, author={Ray, Chelsie Batten and Hedges, Allison and Stitzinger, Ernest}, year={2014}, month={Apr}, pages={703–712} }
@article{batten_bosko-dunbar_hedges_hird_stagg_stitzinger_2013, title={A FRATTINI THEORY FOR LEIBNIZ ALGEBRAS}, volume={41}, ISSN={["1532-4125"]}, DOI={10.1080/00927872.2011.643844}, abstractNote={A Frattini theory for non-associative algebras was developed in [13 Towers , D. ( 1973 ). A Frattini theory for algebras . Proc. London Math. Soc. 27 : 440 – 462 .[Crossref], [Web of Science ®] , [Google Scholar]] and results for particular classes of algebras have appeared in various articles. Especially plentiful are results on Lie algebras. It is the purpose of this paper to extend some of the Lie algebra results to Leibniz algebras.}, number={4}, journal={COMMUNICATIONS IN ALGEBRA}, author={Batten, Chelsie and Bosko-Dunbar, Lindsey and Hedges, Allison and Hird, J. T. and Stagg, Kristen and Stitzinger, Ernest}, year={2013}, month={Apr}, pages={1547–1557} }
@article{hird_jing_stitzinger_2012, title={CODES AND SHIFTED CODES}, volume={22}, ISSN={["1793-6500"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84865779191&partnerID=MN8TOARS}, DOI={10.1142/s0218196712500543}, abstractNote={The action of the Bernstein operators on Schur functions was given in terms of codes by Carrell and Goulden (2011) and extended to the analog in Schur Q-functions in our previous work. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.}, number={6}, journal={INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION}, author={Hird, J. T. and Jing, Naihuan and Stitzinger, Ernest}, year={2012}, month={Sep} }
@article{hird_jing_stitzinger_2011, title={CODES AND SHIFTED CODES OF PARTITIONS}, volume={21}, ISSN={["1793-6500"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84555186874&partnerID=MN8TOARS}, DOI={10.1142/s0218196711006595}, abstractNote={In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's Theorem. We show that this identity is a straightforward consequence of the classical result. We also show how a similar approach using the codes of partitions can be generalized from Schur functions to also include Schur $Q$-functions and derive the combinatorial formulation for both cases. We then apply them by examining the Littlewood-Richardson and Pieri Rules.}, number={8}, journal={INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION}, author={Hird, J. T. and Jing, Naihuan and Stitzinger, Ernest}, year={2011}, month={Dec}, pages={1447–1462} }
@article{stagg_stitzinger_2011, title={MINIMAL NON-ELEMENTARY LIE ALGEBRAS}, volume={139}, ISSN={["0002-9939"]}, DOI={10.1090/s0002-9939-2010-10711-6}, abstractNote={Minimal non-elementarty finite groups must be nilpotent. The Lie algebra analogue admits non-nilpotent examples. We classify them for complex solvable Lie algebras.}, number={7}, journal={PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Stagg, Kristen and Stitzinger, Ernest}, year={2011}, month={Jul}, pages={2435–2437} }
@article{stitzinger_zack_2009, title={Realizations of the complex nilpotent lie algebras with small second derived quotient}, volume={18}, DOI={10.13001/1081-3810.1328}, abstractNote={The fourteen complex nilpotent Lie algebras with a small derived quotient arerealized here using 7x7 matrices.}, journal={Electronic Journal of Linear Algebra}, author={Stitzinger, Ernest and Zack, L.}, year={2009}, pages={513–515} }
@book{klima_sigmon_stitzinger_2007, title={Applications of abstract algebra with Maple and MATLAB2007}, publisher={Boca Raton: Chapman & Hall/CRC}, author={Klima, R.E. and Sigmon, N.P. and Stitzinger, E.L.}, year={2007} }
@article{bradley_stitzinger_2007, title={Class, dimension and length in nilpotent lie algebras}, volume={16}, DOI={10.13001/1081-3810.1212}, abstractNote={The problem of finding the smallest order of a p-group of a given derived length hasa long history. Nilpotent Lie algebra versions of this and related problems are considered. Thus,the smallest order of a p-group is replaced by the smallest dimension of a nilpotent Lie algebra. Foreach length t, an upper bound for this smallest dimension is found. Also, it is shown that for eacht ≥ 5 there is a two generated Lie algebra of nilpotent class d = 21(2t−5) whose derived length is t.For two generated Lie algebras, this result is best possible. Results for small t are also found. Theresults are obtained by constructing Lie algebras of strictly upper triangular matrices.}, journal={Electronic Journal of Linear Algebra}, author={Bradley, L. W. and Stitzinger, Ernest}, year={2007}, pages={429–434} }
@article{kim_misra_stitzinger_2004, title={On the nilpotency of certain subalgebras of Kac-Moody Lie algebras}, volume={14}, number={1}, journal={Journal of Lie Theory}, author={Kim, Y. and Misra, K. C. and Stitzinger, E.}, year={2004}, pages={23-} }
@article{holmes_stitzinger_2001, title={Finite dimensional nilpotent Lie algebras with isomorphic maximal subalgebras}, volume={29}, ISSN={["0092-7872"]}, DOI={10.1081/AGB-100002404}, abstractNote={Nilpotent Lie algebras with maximal subalgebras are considered. A bound on the dimension of these algebras as a function of their coclass is obtained. These algebras are then classified up to coclass two. The result is field dependent and several fields are considered.}, number={6}, journal={COMMUNICATIONS IN ALGEBRA}, author={Holmes, K and Stitzinger, E}, year={2001}, pages={2501–2521} }
@book{klima_sigmon_stitzinger_2000, title={Applications of abstract algebra with Maple}, ISBN={0849381703}, publisher={Boca Raton, FL: CRC Press}, author={Klima, R. E. and Sigmon, N. and Stitzinger, E.}, year={2000} }
@article{stitzinger_turner_1999, title={Concerning derivations of lie algebras}, volume={45}, DOI={10.1080/03081089908818596}, abstractNote={Schur showed that if the center of a group has finite index, then the commutator subgroup is finite. By replacing inner automorphisms by automorphisms, Hegarty obtained a variation of Schur's result. The Lie algebra analogue of Schur's result is well-known. We obtain a strong Lie algebra version of Hegarty's result.}, number={1999}, journal={Linear & Multilinear Algebra}, author={Stitzinger, Ernest and Turner, R.}, year={1999}, pages={329–331} }
@article{hardy_stitzinger_1998, title={On characterizing nilpotent lie algebras by their multipliers, t(L) = 3,4,5,6}, volume={26}, ISSN={["1532-4125"]}, DOI={10.1080/00927879808826357}, abstractNote={The nilpotent Lie algebras L of dimension n whose multipliers have dimension ½n(n-1)-t(L) have been found in [2] for t(L) = 0,1,2. Using a different method, we find similar results for t(L) = 3,4,5,6. The first author is extending the results to t(L) = 7 and 8.}, number={11}, journal={COMMUNICATIONS IN ALGEBRA}, author={Hardy, P and Stitzinger, E}, year={1998}, pages={3527–3539} }
@article{batten_moneyhun_stitzinger_1996, title={On characterizing nilpotent Lie algebras by their multipliers}, volume={24}, ISSN={["0092-7872"]}, DOI={10.1080/00927879608825817}, abstractNote={Abstract In recent work, groups of order pj whose multiplier has order , have been classified when t(G) = 0 or 1 in [2] and when t(G) = 2 in [6]. It is the purpose of this paper to obtain similar results for Lie algebras.}, number={14}, journal={COMMUNICATIONS IN ALGEBRA}, author={Batten, P and Moneyhun, K and Stitzinger, E}, year={1996}, pages={4319–4330} }
@article{batten_stitzinger_1996, title={On covers of Lie algebras}, volume={24}, ISSN={["0092-7872"]}, DOI={10.1080/00927879608825816}, abstractNote={Abstract In dealing with the central extensions of a finite group G one finds that although covers need not be isomorphic, for each such H there exists a cover for which H is a. homomorphic image [1]. For finite dimensional Lie algebras, covers are isomorphic. We shall show that the second property also holds for Lie algebras. Thus to find all such extensions one needs to compute the cover and consider ideals contained in the multiplier (kernel of the homomorphism). Several examples are constructed. Our Lie algebras are taken over a field.}, number={14}, journal={COMMUNICATIONS IN ALGEBRA}, author={Batten, P and Stitzinger, E}, year={1996}, pages={4301–4317} }
@article{stitzinger_1987, title={The probability that a linear system is consistent}, volume={21}, ISSN={0308-1087 1563-5139}, url={http://dx.doi.org/10.1080/03081088708817811}, DOI={10.1080/03081088708817811}, abstractNote={Pertaining to his work on cryptography, Jack Levine recently asked the following question. If one randomly chooses a system of 10 equations and 4 unknowns with coefficients from the integers modulo n, then what is the probability that one has chosen a consistent system? This paper answers this question. Counting arguments involving elementary linear algebra are the only tools needed.}, number={4}, journal={Linear and Multilinear Algebra}, publisher={Informa UK Limited}, author={Stitzinger, Ernest L.}, year={1987}, month={Dec}, pages={367–371} }