Title: Linear identities and the associated wreath products

Speaker: Petr Vojtechovsky (University of Denver)

Abstract:

An identity is linear if the same variables appear on both sides, each
variable exactly ones.  A wreath product arises from a linear identity
F upon considering all possible applications of F to terms of some
fixed length. We use this wreath product to study F by group
theoretical tools.

As a motivation, we show that there is a unique linear identity that
encompasses both associativity and commutativity, when applied to
sufficiently long terms.

This identity can then be used to shorten equational bases of some
algebras in which associativity and commutativity appear, for instance
in boolean algebras (OTTER says so!).