@article{doubek_lada_2016, title={Homotopy derivations}, volume={11}, ISSN={["1512-2891"]}, DOI={10.1007/s40062-015-0118-7}, abstractNote={We define a strong homotopy derivation of (cohomological) degree k of a strong homotopy algebra over an operad $$\mathcal {P}$$ . This involves resolving the operad obtained from $$\mathcal {P}$$ by adding a generator with "derivation relations". For a wide class of Koszul operads $$\mathcal {P}$$ , in particular $$\mathcal {A}{ss}$$ and $$\mathcal {L}{ie}$$ , we describe the strong homotopy derivations by coderivations and show that they are closed under the Lie bracket. We show that symmetrization of a strong homotopy derivation of an $$A_\infty $$ algebra yields a strong homotopy derivation of the symmetrized $$L_\infty $$ algebra. We give examples of strong homotopy derivations generalizing inner derivations.}, number={3}, journal={JOURNAL OF HOMOTOPY AND RELATED STRUCTURES}, author={Doubek, Martin and Lada, Tom}, year={2016}, month={Sep}, pages={599–630} }
@article{allocca_lada_2010, title={A finite dimensional A(infinity) algebra example}, volume={17}, number={1}, journal={Georgian Mathematical Journal}, author={Allocca, M. P. and Lada, T.}, year={2010}, pages={1–12} }
@article{kadeishvili_lada_2009, title={A small open-closed homotopy algebra (OCHA)}, volume={16}, number={2}, journal={Georgian Mathematical Journal}, author={Kadeishvili, T. and Lada, T.}, year={2009}, pages={305–310} }
@article{daily_lada_2005, title={A finite dimensional L-infinity algebra example in gauge theory}, volume={7}, ISSN={["1532-0081"]}, DOI={10.4310/HHA.2005.v7.n2.a4}, abstractNote={We construct an example of a finite dimensional $L_{\infty}$ algebra which is generated by a Lie algebra together with a non-Lie action on another vector space. We then show how this example fits into the gauge transformation theory of Berends, Burgers and Van Dam.}, number={2}, journal={HOMOLOGY HOMOTOPY AND APPLICATIONS}, author={Daily, Marilyn and Lada, Tom}, year={2005}, pages={87–93} }
@article{lada_markl_2005, title={Symmetric brace algebras}, volume={13}, ISSN={["1572-9095"]}, DOI={10.1007/s10485-005-0911-2}, abstractNote={We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin.}, number={4}, journal={APPLIED CATEGORICAL STRUCTURES}, author={Lada, T and Markl, M}, year={2005}, month={Aug}, pages={351–370} }
@article{fulp_lada_stasheff_2002, title={sh-Lie algebras induced by gauge transformations}, volume={231}, ISSN={["0010-3616"]}, DOI={10.1007/s00220-002-0678-3}, abstractNote={Traditionally symmetries of field theories are encoded via Lie group actions, or more generally, as Lie algebra actions. A significant generalization is required when “gauge parameters” act in a field dependent way. Such symmetries appear in several field theories, most notably in a “Poisson induced” class due to Schaller and Strobl [SS94] and to Ikeda [Ike94], and employed by Cattaneo and Felder [CF99] to implement Kontsevich's deformation quantization [Kon97]. Consideration of “particles of spin > 2” led Berends, Burgers and van Dam [Bur85,BBvD84,BBvD85] to study “field dependent parameters” in a setting permitting an analysis in terms of smooth functions. Having recognized the resulting structure as that of an sh-Lie algebra (L ∞-algebra), we have now formulated such structures entirely algebraically and applied it to a more general class of theories with field dependent symmetries.}, number={1}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Fulp, R and Lada, T and Stasheff, J}, year={2002}, month={Nov}, pages={25–43} }
@article{barnich_fulp_lada_stasheff_2000, title={Algebra structures on Hom (C, L)}, volume={28}, ISSN={["0092-7872"]}, DOI={10.1080/00927870008827169}, abstractNote={We consider the space of linear maps from a coassociative coalgebra C into a Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry properties of the induced bracket on Hom(C L) fail to hold. We define the concept of twisted domain (TD) algebras in order to recover the symmetries and also construct a modified Chevalley-Eilenbcrg complex in order to define the cohomology of such algebras.}, number={11}, journal={COMMUNICATIONS IN ALGEBRA}, author={Barnich, G and Fulp, R and Lada, T and Stasheff, J}, year={2000}, pages={5481–5501} }
@article{marra_1999, title={Factors affecting the adoption of transgenic crops: Some evidence from southeastern US cotton farmers}, volume={1}, journal={AgBioTechNet: The Online Service for Agricultural Biotechnology}, author={Marra, M. C.}, year={1999}, pages={1} }
@article{barnich_fulp_lada_stasheff_1998, title={The sh Lie structure of Poisson brackets in field theory}, volume={191}, ISSN={["0010-3616"]}, DOI={10.1007/s002200050278}, abstractNote={A general construction of an sh Lie algebra (L ∞-algebra) from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.}, number={3}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Barnich, G and Fulp, R and Lada, T and Stasheff, J}, year={1998}, month={Feb}, pages={585–601} }