Evaluations of nonassociative polynomials on finite dimensional algebras

Авторы: Kanel-Belov Alexei, Malev Sergey
Сборник: International Conference on Ring Theory Shirshov-2021 dedicated to the 100th anniversary of A. I. Shirshov (1921-1981)
Тезисы
Год издания: 2021
Издательство: ИЦиГ СО РАН
Местоположение издательства: Новосибирск
Первая страница: 15
Последняя страница: 15
Аннотация: Let p be a polynomial in several non-commuting variables with coefficients in analgebraically closed field K of arbitrary characteristic. It has been conjectured that for any n, forp multilinear, the image of p evaluated on the set Mn(K) of n by n matrices is either zero, or theset of scalar matrices, or the set sln(K) of matrices of trace 0, or all of Mn(K).In this talk we will discuss the generalization of this conjecture for non-associativealgebras such as Cayley-Dickson algebra (i.e. algebra of octonions), pure (scalar free) octonionMalcev algebra and basic low rank Jordan algebras.Alexei Kanel-Belov, Sergey Malev, Louis Rowen, Roman Yavich, “Evaluations ofnoncommutative polynomials on algebras: Methods and problems, and the Lvov-KaplanskyConjecture”, Symmetry Integrability Geom. Methods Applications,, 16 (2020), 071 , 61 pp.,Special Issue on Algebra, Topology, and Dynamics in Interaction in honor of Dmitry Fuchs.
Добавил в систему: Белов Алексей Яковлевич

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