What question did this study set out to answer?

This research aims to characterize varieties of graded algebras with multiplicities bounded by a constant in finite groups.

May 16, 2026

Algebras with additional structures and multiplicities bounded by a constant

Puntos clave

This research aims to characterize varieties of graded algebras with multiplicities bounded by a constant in finite groups.
Analyzed finite groups and graded algebras over a field of characteristic zero.
Characterized varieties using algebraic identities and cocharacters.
Provided explicit polynomial identities for graded algebras with certain involutions.
Identified specific algebraic identities for varieties of graded algebras with bounded multiplicities.
Determined conditions for the existence of graded involutions in algebras.
Established a comprehensive list of polynomial identities satisfying the characterized varieties.

Resumen

Let Formula: see text be a finite group and Formula: see text a Formula: see text-graded algebra over a field Formula: see text of characteristic zero. We characterize the varieties of Formula: see text-graded algebras such that the multiplicities Formula: see text appearing in the Formula: see text-cocharacters of Formula: see text are bounded by a constant, in terms of Formula: see text-identities. If Formula: see text is endowed with a graded involution ∗, i.e. if Formula: see text is a Formula: see text-algebra, we characterize the varieties of Formula: see text-algebras whose multiplicities in the sequence of Formula: see text-cocharacters of Formula: see text are bounded by Formula: see text by explicitly providing a list of Formula: see text-polynomial identities satisfied by such varieties.

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Cite This Study

Santos et al. (Thu,) studied this question.

synapsesocial.com/papers/6a080985a487c87a6a40b7a6 https://doi.org/https://doi.org/10.1142/s0218196726500360

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