Graded identities of matrix algebras and the universal graded algebra

DOI10.1090/S0002-9947-10-04811-7zbMath1203.16020arXiv0710.5568OpenAlexW2004912230MaRDI QIDQ3566709

Michael Natapov, Eli Aljadeff, Darrell E. Haile

Publication date: 8 June 2010

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

Full work available at URL: https://arxiv.org/abs/0710.5568

zbMATH Keywords

central simple algebrasgraded polynomial identitiesSpecht problemfine gradingsgeneric division algebrasgroup gradings on matrix algebras

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Graded rings and modules (associative rings and algebras) (16W50) Finite-dimensional division rings (16K20) (T)-ideals, identities, varieties of associative rings and algebras (16R10) Twisted and skew group rings, crossed products (16S35)

Related Items (23)

Generic base algebras and universal comodule algebras for some finite-dimensional Hopf algebras ⋮ Verbally prime T-ideals and graded division algebras ⋮ Crossed products and their central polynomials. ⋮ Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras. ⋮ Graded embeddings of finite dimensional simple graded algebras. ⋮ On weak equivalences of gradings ⋮ Descent, fields of invariants, and generic forms via symmetric monoidal categories ⋮ On graded associative algebras. ⋮ Upper triangular matrices of graded division algebras and their identities ⋮ Representability and Specht problem for \(G\)-graded algebras. ⋮ On the structure of graded commutative algebras ⋮ Polynomial identities and noncommutative versal torsors. ⋮ Groups of central-type, maximal connected gradings and intrinsic fundamental groups of complex semisimple algebras ⋮ Simple 𝐺-graded algebras and their polynomial identities ⋮ Orthogonal-gradings on \(H^*\)-algebras ⋮ Group graded PI-algebras and their codimension growth. ⋮ Identities and isomorphisms of graded simple algebras. ⋮ The Noether problem for Hopf algebras ⋮ Graded polynomial identities and exponential growth ⋮ Hopf cocycle deformations and invariant theory ⋮ On regular 𝐺-gradings ⋮ Group Gradings on Finite Dimensional Lie Algebras ⋮ On generic \(G\)-graded Azumaya algebras

Cites Work

• Polynomial identities and noncommutative versal torsors.
• Projective bases of division algebras and groups of central type. II.
• A method of construction of finite-dimensional triangular semisimple Hopf algebras
• Projective bases of division algebras and groups of central type.
• Projective Schur algebras of nilpotent type are Brauer equivalent to radical algebras
• On groups of central type
• Graded polynomial identities of matrices
• Finite groups with an irreducible representation of large degree
• Separable algebras over commutative rings
• Group Gradings on Matrix Algebras
• Division algebras with a projective basis
• Group gradings on associative algebras
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