Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ,
Keywords: ring theory, Jordan algebras, Banah algebras, Lie algebras, coalgebras.
Subject:
A class of Jordan bialgebras related to the "Jordan analog" of the classical Yang–Baxter equation was introduced. It had proved this every Jordan bialgebra defined on a finite-dimensional semisimple Jordan algebra belongs to that class. The triangle and the quasitriangle Jordan bialgebras were defined in agreement with corresponding concepts for the Lie bialgebras, and a characterization the finite-dimensional Jordan algebras admitting a nontrivial structure of a quasitriangle bialgebra was obtained.
Main publications:
On a class of Jordan D-bialgebras // St. Petersburg Math. J., 2000, 11, 4, 589–609.
Jordan D-bialgebras and sympectic forms on Jordan algebras // Siberian Advances in Mathematics, 2000, 10, 2, 134–142.
Jordan bialgebras and their relation to Lie bialgebras // Algebra and Logic, 1997, 36, 1, 3–25.
Finite-Dimensional Jordan Algebras Admitting the Structure of a Jordan Bialgebra // Algebra and Logic, 1999, 38, 1, 40–67.
