## 2007.33: Algebraic structures connected with pairs of compatible associative algebras

2007.33:
Alexander Odesskii and Vladimir Sokolov
(2006)
*Algebraic structures connected with pairs of compatible associative algebras.*
International Mathematics Research Notices, 2006.
pp. 1-35.
ISSN 1073-7928

Full text available as:

PDF - Archive staff only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 714 Kb |

## Abstract

We study associative multiplications in semisimple associative algebras over ℂ compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over ℂ. It turns out that these deformations are in one-to-one correspondence with representations of certain algebraic structures, which we call M-structures in the matrix case and PM-structures in the case of direct sums of several matrix algebras. We also investigate various properties of PM-structures, provide numerous examples and describe an important class of PM-structures. The classification of these PM-structures naturally leads to affine Dynkin diagrams of A,D,E-types.

Item Type: | Article |
---|---|

Subjects: | MSC 2000 > 14 Algebraic geometry MSC 2000 > 17 Nonassociative rings and algebras |

MIMS number: | 2007.33 |

Deposited By: | Miss Louise Stait |

Deposited On: | 27 March 2007 |

Download Statistics: last 4 weeks

Repository Staff Only: edit this item