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 with 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 role in various areas of mathematics, including noncommutative analysis in the context of \(C^{\ast}\)-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 \(f(x_1, \dots , x_n)\) 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.

Día

Martes, 22 de abril de 2025

Lugar

Aula 7
Facultade de Matemáticas