2025/12/05 by Cota, Wesley Quaresma, Santos, Rafael Bezerra dos, Vieira, Ana Cristina
Computer Science · Mathematics · #16R50 #16W50 #20C30 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16R10 #Rings and Algebras (math.RA) #Secondary 16W10
paper · doi:10.48550/arxiv.2512.06164
openalex publication_date 2025/12/05 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28
In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded involution, called (G,*)-algebras. We give an explicit description of the decomposition of the ⟨ n ⟩-cocharacter for some important (G,*)-algebras A, for every ⟨ n ⟩=(n1, …, n2t). For each algebra A, the nth colength is defined as the number of irreducible components that appear in these decompositions. Our aim is to classify varieties whose nth colengths are bounded by a fixed constant.