@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 ∞ 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. L ∞ algebrasWe begin by recalling the definition of an L ∞ algebra [7], [9].Let V be a graded vector space over a field k.}, number={2}, journal={HOMOLOGY HOMOTOPY AND APPLICATIONS}, author={Daily, Marilyn and Lada, Tom}, year={2005}, pages={87–93} }
@article{daily_2004, title={L-infinity structures on spaces with three one-dimensional components}, volume={32}, ISSN={["0092-7872"]}, DOI={10.1081/AGB-120029922}, abstractNote={Abstract L ∞ structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of L n and L ∞ structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify all possible L n and L ∞ structures on V = V m ⊕ V m+1 ⊕ V m+2 when each of the three components is one-dimensional. Included are necessary and sufficient conditions under which a space with an L 3 structure is a differential graded Lie algebra. It is also shown that some of these differential graded Lie algebras possess a nontrivial L n structure for higher n.}, number={5}, journal={COMMUNICATIONS IN ALGEBRA}, author={Daily, M}, year={2004}, pages={2041–2059} }