2005/12/21 by Alexander Odesskii, Vladimir Sokolov, В. В. Соколов +2 · 1 citation
Mathematics · Physics and Astronomy · #14H70 #17B63 #17B80 #32L81 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #hep-th #math.QA #math.RA #math.RT #msc:14H70 #msc:17B63 #msc:17B80 #msc:32L81 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0512499
29 pages, Latex. The case of semi-simple algebras A and B is completed (Chapter 4). A construction of compatible products is added (Chapter 1)
openalex publication_date 2005/12/21 · arxiv created 2006/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study associative multiplications in semi-simple 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-type.