Varieties of graded W-algebras and asymptotic behavior of codimension growth

2025/11/27 by Giovanni Busalacchi, Busalacchi, Giovanni, Fabrizio Martino +3
Mathematics · #16D20 #16R50 #16W50 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16R10 #Rings and Algebras (math.RA) #Secondary 16P90

paper · pdf · doi:10.48550/arxiv.2511.22602

openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

Let W be a G-graded algebra over a field of characteristic zero, where G is a finite group. We develope a theory of generalized G-graded polynomial identities satisfied by any finite-dimensional W-algebra A, by mean of the graded multiplier algebra of A. In particular, we first prove that the graded generalized exponent exists and equals the ordinary one. Then, we explicitly compute the G-graded generalized identities of UT₂, the 2 × 2 upper triangular matrix algebra equipped with its canonical ℤ₂-grading, under all the possible graded W-actions. Finally, we exhibit examples of varieties of graded W-algebras with almost polynomial growth of the codimensions.

Citations

• Multipliers, W-algebras and the growth of generalized polynomial identities
• Multialternating graded polynomials and growth of polynomial identities

Related

• Group graded algebras and varieties with quadratic codimension growth
• Multialternating graded polynomials and growth of polynomial identities
• Multipliers, W-algebras and the growth of generalized polynomial identities
• Graded polynomial identities and exponential growth
• POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH