Work

Multipliers, W‐algebras, and the growth of generalized polynomial identities

Year: 2026

Type: article

Abstract: Let be a ‐algebra over a field of characteristic zero, where is any ‐algebra. We first develop a comprehensive theory of generalized identities independent of the algebraic structure of , using the multiplier algebra of . Then, we investigate the generalized variety generated by the matrix algebra with a suitable action, proving that it exhibits almost polynomial growth of the generalized codimensions. Furthermore, we characterize the generalized varieties of almost polynomial growth generated by finite‐dimensional ‐algebras. Finally, we provide a counterexample to the Specht property of generalized ‐ideals in characteristic zero.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70531

Authors: Fabrizio Martino, Carla Rizzo

Institutions: University of Palermo, Centro de Matemática, University of Coimbra

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Universidade de Coimbra, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, Fundação para a Ciência e a Tecnologia

Awards: Centro de Matemática da Universidade de Coimbra, G6265307419, G6997658380