Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

DOI10.1090/S0002-9947-08-04500-5zbMath1161.16016MaRDI QIDQ3533828

Allan Berele, Amitai Regev

Publication date: 24 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

codimension sequencesfinitely generated algebrasalgebras with polynomial identityCapelli identitiesasymptotics of codimensions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Representations of finite symmetric groups (20C30) Growth rate, Gelfand-Kirillov dimension (16P90) Trace rings and invariant theory (associative rings and algebras) (16R30) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items

Codimension sequences and their asymptotic behavior ⋮ Regev's conjecture for algebras with Hopf actions ⋮ Central polynomials of algebras and their growth ⋮ On the codimension sequence of \(G\)-simple algebras. ⋮ Codimension growth of simple Jordan superalgebras ⋮ Superalgebras: polynomial identities and asymptotics ⋮ Anomalies on codimension growth of algebras. ⋮ A finiteness criterion and asymptotics for codimensions of generalized identities. ⋮ Star-polynomial identities: computing the exponential growth of the codimensions ⋮ Exponential growth of codimensions of identities of algebras with unity ⋮ Polynomial identities and algebraic combinatorics on words ⋮ Algebraic properties of codimension series of PI-algebras. ⋮ Growth for algebras satisfying polynomial identities. ⋮ Hilbert series of \(T\)-spaces ⋮ Asymptotic behavior of \(S_n\) degrees associated with rational functions. ⋮ Codimensions of algebras with additional structures ⋮ Trace codimensions of algebras and their exponential growth ⋮ A graph theoretic approach to graded identities for matrices. ⋮ Asymptotics of graded codimension of upper triangular matrices ⋮ Star-fundamental algebras: polynomial identities and asymptotics ⋮ Properties of hook Schur functions with applications to P. I. algebras ⋮ Regev's and Amitsur's conjectures for codimensions of generalized polynomial identities. ⋮ COCHARACTERS OF POLYNOMIAL IDENTITIES OF UPPER TRIANGULAR MATRICES ⋮ Zariski closed algebras in varieties of universal algebra. ⋮ Central polynomials of associative algebras and their growth ⋮ The polynomial part of the codimension growth of affine PI algebras ⋮ A characterization of *-minimal algebras with involution. ⋮ Finite-dimensional non-associative algebras and codimension growth ⋮ Identities of *-superalgebras and almost polynomial growth ⋮ On PI-algebras with additional structures: rationality of Hilbert series and Specht's problem ⋮ Understanding star-fundamental algebras ⋮ Growth of polynomial identities: is the sequence of codimensions eventually non-decreasing? ⋮ Cocharacters of polynomial identities of block triangular matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Codimensions of T-ideals and Hilbert series of relatively free algebras
• Asymptotics and algebraicity of some generating functions
• Algebras satisfying a Capelli identity
• Asymptotic estimates using probability
• Codimensions of products and of intersections of verbally prime T-ideals
• On codimension growth of finitely generated associative algebras
• Exponential codimension growth of PI algebras: an exact estimate
• Multiplicities of Schur functions in invariants of two \(3\times 3\) matrices
• Asymptotic values for degrees associated with strips of Young diagrams
• Applications of Belov's theorem to the cocharacter sequence of p.i. algebras.
• On the rationality of Hilbert series of relatively free algebras
• Lectures on Polytopes
• Approximate multiplicities in the trace cocharacter sequence of two three-by-three matrices
• Exponential growth for codimensions of some p. i. algebras