DEFORMATION THEORY OF INFINITY ALGEBRAS

By Alice Fialowski, M. Penkava. 2001

58 citations recorded by the source corpus.

Abstract This work explores the deformation theory of algebraic structures in a very general setting. These structures include associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. In all these cases the algebraic structure is determined by an element of a certain graded Lie algebra which determines a differential on the Lie algebra. We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation. By working at this level of generality, the main ideas involved in deformation theory stand out more clearly.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cbba7e36691094fa2f979242de3068e80a80b68c

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In Algebra and Number Theory

1. M. Ammar
2. Norbert Poncin

In Geometry and Topology

1. M. Ammar
2. Norbert Poncin

In Mathematical Physics

1. M. Ammar
2. Norbert Poncin

Citations in the corpus

• Coalgebraic Approach to the Loday Infinity Category, Stem Differential for 2n-ary Graded and Homotopy Algebras (2008, methodology): “in [LMS92]) [resp. in [Pen01] and [ FP02 ]]. Further, graded Poisson and Jacobi cohomologies were define d purely algebraically by Grabowski and Marmo in [GM03].”