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This is a Quantitative Study study.

October 10, 2025Open Access

Algebras with additional structures and multiplicities bounded by a constant

Key Points

The study finds that certain varieties of g-graded algebras have bounded multiplicities, revealing underlying algebraic structures.
Characterization utilizes g-identities to describe the relationships between the algebraic properties and their multiplicities.
A specific focus is placed on (G,*)-algebras, showing the distinct polynomial identities that govern their bounded multiplicities.
Understanding these constraints sheds light on algebra behavior, supporting future research in algebraic structures and their applications.

Abstract

G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the varieties of G-graded algebras such that the multiplicities m ⏚ appering in the n -cocharacters of A are bounded by a constant, in terms of G-identities. If A is endowed with a graded involution, i. e. if A is a (G, ) -algebra, we characterize the varieties of (G, *) -algebras whose multiplicities in the sequence of n-cocharacters of A are bounded by 1 by showing a list of (G, ) -polynomial identities satisfied by such varieties.

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