Graded Polynomial Identities for Tensor Products by the Grassmann Algebra

DOI10.1081/AGB-120017775zbMath1039.16023MaRDI QIDQ4802447

Vincenzo C. Nardozza

Publication date: 14 April 2003

Published in: Communications in Algebra (Search for Journal in Brave)

zbMATH Keywords

graded identitiescocharacter sequencesGrassmann algebragraded cocharactersgraded PI algebras

Mathematics Subject Classification ID

Actions of groups and semigroups; invariant theory (associative rings and algebras) (16W22) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Graded rings and modules (associative rings and algebras) (16W50) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Exterior algebra, Grassmann algebras (15A75)

Related Items (22)

Tensor product theorems in positive characteristic. ⋮ Graded identities for algebras with elementary gradings over an infinite field ⋮ Polynomial identities of algebras in positive characteristic. ⋮ Automorphisms and superalgebra structures on the Grassmann algebra ⋮ PI non-equivalence in positive characteristic. ⋮ Unnamed Item ⋮ Graded identities and central polynomials for the verbally prime algebras ⋮ The GK dimension of relatively free algebras of PI-algebras ⋮ On \(\mathbb Z_2\)-graded identities of \(UT_2(E)\) and their growth. ⋮ On a Regev-Seeman conjecture about \(\mathbb{Z}_2\)-graded tensor products. ⋮ GRADED POLYNOMIAL IDENTITIES OF VERBALLY PRIME ALGEBRAS ⋮ GRADED IDENTITIES AND PI EQUIVALENCE OF ALGEBRAS IN POSITIVE CHARACTERISTIC ⋮ Graded identities of block-triangular matrices ⋮ Graded identities of several tensor products of the Grassmann algebra ⋮ Ordinary and ℤ₂-Graded Cocharacters ofUT₂(E) ⋮ GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD ⋮ PI (non)equivalence and Gelfand-Kirillov dimension in positive characteristic. ⋮ Identities of PI-Algebras Graded by a Finite Abelian Group ⋮ The graded Gelfand--Kirillov dimension of verbally prime algebras ⋮ Graded identities for tensor products of matrix (super)algebras over the Grassmann algebra ⋮ A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS ⋮ \(\mathbb{Z}_{k+l}\times\mathbb{Z}_2\)-graded polynomial identities for \(M_{k,l}(E)\otimes E\).

Cites Work

• Codimensions and trace codimensions of matrices are asymptotically equal
• Magnum P.I
• On the identities of subalgebras of matrices over the Grassmann algebra
• Cocharacters of \(\mathbb Z/2\mathbb Z\)-graded algebras
• Group-graded algebras with polynomial identity
• Exponential codimension growth of PI algebras: an exact estimate
• On the graded identities of \(M_{1,1}(E)\)
• Tensor products of matrix algebras over the Grassmann algebra
• POLYNOMIAL IDENTITIES ON SUPERALGEBRAS AND ALMOST POLYNOMIAL GROWTH
• Group Actions and Asymptotic Behavior of Graded Polynomial Identities
• $\mathbf {Z}_n$-graded polynomial identities of the full matrix algebra of order $n$
• Cocharacters of g-graded algebras
• Z-Graded Polynomial Identities of the Full Matrix Algebra

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