Deformation theory and Lie algebra homology
Vladimir Hinich, Vadim Schechtman
TL;DR
This paper explores the use of Lie algebra homology to describe the structure of functions on the base of universal formal deformations in various moduli problems, linking deformation theory with homological algebra.
Contribution
It provides a canonical homological description of the deformation base via dg Lie algebra homology, offering a new perspective on deformation problems.
Findings
Homology groups characterize deformation bases
Canonical dg Lie algebra associated with moduli problems
Homological methods unify deformation descriptions
Abstract
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique quasi-isomorphism) associated with a problem.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models