Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras.

DOI10.1007/BF02773825zbMath1138.16009OpenAlexW2007984195MaRDI QIDQ2472741

Francesca Saviella Benanti, I. Yu. Sviridova

Publication date: 22 February 2008

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02773825

zbMATH Keywords

Grassmann algebrasCapelli identityAmitsur-Capelli polynomialscodimension sequencesT-prime algebrasverbally prime PI-algebrasasymptotic behaviour of codimensions

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Trace rings and invariant theory (associative rings and algebras) (16R30) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Exterior algebra, Grassmann algebras (15A75) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

Related Items (5)

On the asymptotics of Capelli polynomials ⋮ *-Graded Capelli polynomials and their asymptotics ⋮ Capelli identities on algebras with involution or graded involution ⋮ Asymptotics for graded Capelli polynomials. ⋮ Asymptotics for Capelli polynomials with involution

Cites Work

• A conjecture of Regev about the Capelli polynomial
• Codimensions and trace codimensions of matrices are asymptotically equal
• Invariants and the ring of generic matrices
• On the identities of subalgebras of matrices over the Grassmann algebra
• Algebras satisfying a Capelli identity
• PI-algebras and their cocharacters
• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• Asymptotics for the standard and the Capelli identities.
• On the codimensions of the verbally prime P.I. algebras
• Existence of identities in \(A \otimes B\)
• Identities of associative algebras
• Minimal varieties of algebras of exponential growth
• Exponential growth for codimensions of some p. i. algebras

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