Pseudo-composition algebras as axial algebras

Abstract: We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called PC(η)-axial algebras, where η is an element of the ground field. As a first step towards their classification, we describe 2− and 3-generated subalgebras of such algebras.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar