On the lengths of Okubo algebras

Abstract: The length function of a non-associative algebra describes the guaranteed number of multiplications which will be sufficient to generate the whole algebra with its arbitrary generating set. In this talk we present a new method for length computation based on the sequence of differences between the dimensions of a certain sequence of subspaces. It allows us to compute the length of an Okubo algebra A over an arbitrary field. Namely, if A contains either nonzero idempotents or zero divisors, then its length equals four, and otherwise its length equals three. We also show that, in the latter case, A is generated by any two elements which do not belong to the same two-dimensional subalgebra. The talk is based on a joint work with Alexander Guterman.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar