Semiassociative algebras over a field

Abstract: Associative central simple algebras are a classical subject, related to many areas of study including Galois cohomology and algebraic geometry. An associative central simple algebra is a form of matrices because a maximal étale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of view, we study nonassociative algebras whose nucleus contains an étale subalgebra bi-acting faithfully on the algebra. We show that these algebras, termed semiassociative, are forms of a nonassociative analogue of matrix algebras. Finally, we consider the monoid composed of semiassociative algebras modulo the nonassociative matrix algebras, and discuss its connection to the classical Brauer group. Based on joint work with Darrell Haile, Eliyahu Matzri, Edan Rein and Uzi Vishne.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar