Bulletin of the London Mathematical Society· 2026Q1
Multipliers, W‐algebras, and the growth of generalized polynomial identities
- 3citations
- Q1SCImago
- 2026year
Short summary
A new theory of generalized polynomial identities is developed for W-algebras, showing that the generalized variety generated by a specific matrix algebra exhibits almost polynomial growth of generalized codimensions.
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Key points
- A theory of generalized polynomial identities is established for W-algebras using multiplier algebras.
- The generalized variety generated by M_2(F) with a suitable action shows almost polynomial growth of generalized codimensions.
- Generalized varieties of almost polynomial growth are characterized for finite-dimensional W-algebras.
- A counterexample to the Specht property of generalized W-ideals in characteristic zero is provided.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics