Algebras satisfying a Capelli identity

DOI10.1007/BF02760555zbMath0422.16008MaRDI QIDQ1133606

Amitai Regev

Publication date: 1979

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

zbMATH Keywords

Young diagramT-idealsirreducible characterheight of cocharacter

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Rings with polynomial identity (16Rxx)

Related Items (34)

Growth of central polynomials of verbally prime algebras ⋮ On the asymptotics of Capelli polynomials ⋮ On algebras satisfying symmetric identities ⋮ Polynomial identities for the Jordan algebra of a symmetric bilinear form ⋮ On the identities of subalgebras of matrices over the Grassmann algebra ⋮ Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras ⋮ The mathematics of Amitai Regev ⋮ Growth for algebras satisfying polynomial identities. ⋮ The Kronecker product of \(S_n\)-characters and an \(A\otimes B\) theorem for Capelli identities ⋮ Sign trace identities ⋮ Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities ⋮ Rappresentazioni di gruppi simmetrici ed identita' polinomiali ⋮ PI-algebras and their cocharacters ⋮ COCHARACTERS OF POLYNOMIAL IDENTITIES OF UPPER TRIANGULAR MATRICES ⋮ Modular cocharacters for P. I. algebras ⋮ The exponential growth of codimensions for Capelli identities ⋮ On the cocharacter sequence of 3 × 3 matrices ⋮ Modular representation theory and pi-algebras ⋮ Maximal multiplicities in cocharacter sequences. ⋮ Weak polynomial identities and their applications ⋮ Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras. ⋮ Associative rings ⋮ Cocharacters for the weak polynomial identities of the Lie algebra of \(3 \times 3\) skew-symmetric matrices ⋮ A six generalized squares theorem, with applications to polynomial identity algebras ⋮ Generic verbally prime pi-algebras and their gk-dimensions ⋮ Constructive noncommmutative invariant theory ⋮ On the codimension growth of finite-dimensional Lie algebras ⋮ On codimension growth of finitely generated associative algebras ⋮ Applications of hook Young diagrams to P.I. algebras ⋮ Codimensions and trace codimensions of matrices are asymptotically equal ⋮ Homogeneous polynomial identities ⋮ Wreath products and P.I. algebras ⋮ \(A\)-codimensions and \(A\)-cocharacters ⋮ Cocharacters of polynomial identities of block triangular matrices

Cites Work

• Identities and linear dependence
• The \(T\)-ideal generated by the standard identity \(s_3[x_1,x_2,x_3\)]
• The representations of \(S_n\) and explicit identities for P. I. algebras

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