Algebraic structures connected with pairs of compatible associative algebras
Speaker: Alexander Odesski, Brock University
Abstract: 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.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm