2025/12/04 by Cota, Wesley Quaresma, Yasumura, Felipe
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.04769
openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28
An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence cn(A), n≥ 1, which measures the growth of polynomial identities of a given algebra A. In this context, graded identities naturally arise as prominent tools, since ordinary polynomial identities can be viewed as a particular case of graded identities. Moreover, as an involution does not necessarily preserve the homogeneous components of a grading, it is natural to consider the notion of a homogeneous involution. In this work, we investigate the behavior of the codimension sequence in the setting of G-graded algebras endowed with a homogeneous involution. More specifically, we characterize the varieties of polynomial growth in terms of the exclusion of a list of algebras from the variety. As a consequence, we provide the classification of the varieties with almost polynomial growth in this setting.