On Deformations of Associative Algebras

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to commutativity of the cup-product on Hochschild cohomology, a morphism from the graded algebra Sym(k^n) to Ext^*(A,A), the Ext-algebra in the category of A-bimodules. We prove that any extension of the n-parameter first order deformation of A to an INFINITE ORDER formal deformation provides a canonical `lift' of the graded algebra morphism above to a dg-algebra morphism from Sym(k^n) to the dg-algebra RHom(A,A), where the Symmetric algebra Sym(k^n) is viewed as a dg-algebra (generated by the vector space $\k^n$ placed in degree 2) with zero differential.
A few comments added

Keywords

Quantum Algebra, Algebraic Geometry, K-Theory and Homology, Rings and Algebras

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/101106

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503053
 http://arxiv.org/abs/math/0503053

Collections

arXiv