On Deformations of Associative Algebras
| dc.creator | Bezrukavnikov, Roman | |
| dc.creator | Ginzburg, Victor | |
| dc.date | 2005-03-03 | |
| dc.date | 2006-03-27 | |
| dc.date.accessioned | 2026-07-07T06:39:31Z | |
| dc.date.available | 2026-07-07T06:39:31Z | |
| dc.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. | |
| dc.description | A few comments added | |
| dc.identifier | https://arxiv.org/abs/math/0503053 | |
| dc.identifier | http://arxiv.org/abs/math/0503053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101106 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Rings and Algebras | |
| dc.title | On Deformations of Associative Algebras | |
| dc.type | text |