Minimal varieties of algebras of exponential growth.

DOI10.1016/S0001-8708(02)00047-6zbMath1035.16013MaRDI QIDQ1869995

Antonio Giambruno, Mikhail V. Zaicev

Publication date: 4 May 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

exponentsT-idealsGelfand-Kirillov dimensioncodimension sequencescodimension growthvarieties of associative algebrasrelatively free algebras

Mathematics Subject Classification ID

Growth rate, Gelfand-Kirillov dimension (16P90) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (43)

Central polynomials of algebras and their growth ⋮ \(\mathbb{Z}_2\)-graded cocharacters for superalgebras of triangular matrices. ⋮ Minimal varieties of associative PI (super)-algebras with respect to their (graded) exponent ⋮ Lie solvability and the identity \([x_{1},y_{1}[x_{2},y_{2}]\cdots[x_{q},y_{q}]=0\) in certain matrix algebras] ⋮ Central polynomials and growth functions ⋮ Jordan \((\alpha,\beta)\)-derivations on triangular algebras and related mappings. ⋮ Gelfand-Kirillov dimension of bicommutative algebras ⋮ ℤ2-gradings and minimal varieties of ℤ2-graded PI algebras ⋮ On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups ⋮ Application of Full Quivers of Representations of Algebras, to Polynomial Identities ⋮ Graded polynomial identities on upper block triangular matrix algebras. ⋮ Gradings on block-triangular matrix algebras ⋮ Minimal supervarieties with factorable ideal of graded polynomial identities. ⋮ On some minimal supervarieties of exponential growth. ⋮ Graded identities and isomorphisms on algebras of upper block-triangular matrices ⋮ COCHARACTERS OF POLYNOMIAL IDENTITIES OF UPPER TRIANGULAR MATRICES ⋮ The GK dimension of relatively free algebras of PI-algebras ⋮ Lie solvability in matrix algebras ⋮ Semi-centralizing maps of generalized matrix algebras ⋮ On the factorability of the ideal of \(\ast\)-graded polynomial identities of minimal varieties of PI \(\ast\)-superalgebras ⋮ Central polynomials of associative algebras and their growth ⋮ Proper identities, Lie identities and exponential codimension growth. ⋮ The polynomial part of the codimension growth of affine PI algebras ⋮ On \(\mathbb Z_2\)-graded identities of the super tensor product of \(UT_2(F)\) by the Grassmann algebra. ⋮ Structure of Zariski-closed algebras ⋮ Asymptotic growth of codimensions of identities of associative algebras. ⋮ Minimal varieties of PI-superalgebras with graded involution ⋮ On the number of gradings on matrix algebras ⋮ Codimension growth and minimal superalgebras ⋮ Graded identities of block-triangular matrices ⋮ Asymptotics for the multiplicities in the cocharacters of some PI-algebras ⋮ Graded polynomial identities of triangular algebras ⋮ Lie, Jordan and proper codimensions of associative algebras. ⋮ On the graded identities and cocharacters of the algebra of \(3\times 3\) matrices ⋮ Minimal varieties of associative algebras and transcendental series ⋮ PI-varieties associated to full quivers of representations of algebras ⋮ Full quivers of representations of algebras ⋮ A characterization of minimal varieties of \(\mathbb{Z}_p\)-graded PI algebras ⋮ A characterization of fundamental algebras through \(S_n\)-characters ⋮ Graded involutions on block-triangular matrix algebras ⋮ On the minimal varieties of PI-algebras graded by finite cyclic groups ⋮ Kemer's theorem for affine PI algebras over a field of characteristic zero. ⋮ Cocharacters of polynomial identities of block triangular matrices

Cites Work

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