Deformation of algebra factorisations. (English) Zbl 1003.16024
The paper under review is built on the classical canvas for describing deformations: In the first section, the algebras to be deformed, namely algebra factorisations, are described; (1) a suitable cochain complex is defined; (2) the cohomology of the complex is used to describe the infinitesimal deformations and the obstructions.
The paper ends with three interesting examples: a commutative polynomial algebra, the quantum plane and the quaternion algebra.
The paper ends with three interesting examples: a commutative polynomial algebra, the quantum plane and the quaternion algebra.
Reviewer: Thierry Dana-Picard (Jerusalem)
MSC:
| 16S80 | Deformations of associative rings |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
| 16S40 | Smash products of general Hopf actions |
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
Keywords:
quantum planes; algebra factorisations; cochain complexes; cohomology; infinitesimal deformations; quaternion algebrasReferences:
| [1] | DOI: 10.1007/PL00005530 · Zbl 0979.58002 · doi:10.1007/PL00005530 |
| [2] | Caenepeel S., Factorisation Structures of Algebras and Coalgebras |
| [3] | DOI: 10.1080/00927879508825496 · Zbl 0842.16005 · doi:10.1080/00927879508825496 |
| [4] | Tambara D., J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 37 pp 425– (1990) |
| [5] | DOI: 10.1017/CBO9780511613104 · doi:10.1017/CBO9780511613104 |
| [6] | DOI: 10.1007/s002200050274 · Zbl 0899.55016 · doi:10.1007/s002200050274 |
| [7] | DOI: 10.2307/1970484 · Zbl 0123.03101 · doi:10.2307/1970484 |
| [8] | DOI: 10.1073/pnas.87.1.478 · Zbl 0695.16005 · doi:10.1073/pnas.87.1.478 |
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