Deformation Theory of Infinity Algebras

Details Deformation Theory of Infinity Algebras Deformation Theory of Infinity Algebras

2001-01-11

arxiv.org/abs/math/0101097v1

Journal of Algebra 255 (2002), 59-88

Mathematics

Representation Theory

31 pages, LaTeX2e

Scientific paper

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. In all these cases the algebra structure is determined by an element of a certain graded Lie algebra which plays the role of a differential on this 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.

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