Deformation theory of infinity algebras

Arithmetic Deformation Theory of Lie Algebras

This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...

A-infinity Algebras in Representation Theory

On deformation theory of quantum vertex algebras

We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an associative algebra. We show that this system of equations results from an action principle. This might be the starting point for a p...

Deformation theory via differential graded Lie algebras

This is an expository paper written in 1999 and published in Seminari di Geometria Algebrica 1998-1999, Scuola Normale Superiore (1999). Six years later some arguments used here appear quite naive and obsolete but, in view of the several citations that this paper has obtained in the meantime, I preferred don’t change the mathematical contents and to fix only some typos and minor mistakes. For a...

Exploring Noncommutative Algebras via Deformation Theory

In this lecture 1 I would like to address the following question: given an associative algebra A 0 , what are the possible ways to deform it? Consideration of this question for concrete algebras often leads to interesting mathematical discoveries. I will discuss several approaches to this question, and examples of applying them. 1. Deformation theory 1.1. Formal deformations. The most general a...