Generalized Polynomial Identities and Multiplier Algebras

"Generalized Polynomial Identities and Multiplier Algebras", organizado polo CITMAga en formato presencial. Será impartido por Carla Rizzo (CMUC, Universidade de Coimbra).

Data: 22 de abril  de 2025

Hora: 16:00h  

Duración: 1 hora

Lugar: Aula 7 da Facultade de Matemáticas (USC)

Abstract:

Let W be a unitary associative algebra over a field F of characteristic zero. An associative F-algebra A is called a W-algebra if it is equipped a structure of a W-bimodule satisfying certain additional “associativity conditions”. To formally describe the action of W on A, it is useful to consider the multiplier algebra M(A) of A, a powerful tool that plays a fundamental in various areas of mathematics, including noncommutative analysis in the context of C*-algebras and category theory. Multipliers allow a more flexible approach to structural questions and provide a practical setting for studying identities in W-algebras. Roughly speaking, a generalized polynomial identity (or W-identity) of a W-algebra A is a noncommutative polynomial f(x1,…, xn) in which elements of W appear between the variables and which vanishes under all substitutions of the variables by elements of A. This concept generalizes ordinary polynomial identities, which correspond to the special case when W = F, and provides new insight for understanding the structure of noncommutative algebras.
In this talk, I will present recent advances in the theory of generalized dentities, developed independently of the specific structure of W, focusing on how the multiplier algebra M(A) provides a unifying framework for their study.