Identities and isomorphisms of graded simple algebras.

DOI10.1016/j.laa.2010.01.010zbMath1194.16016OpenAlexW1967760143MaRDI QIDQ968987

Plamen Koshlukov, Mikhail V. Zaicev

Publication date: 11 May 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.01.010

zbMATH Keywords

polynomial identitiesgraded identitiesgraded division algebrasgraded simple algebrasgraded isomorphismsgradings on associative algebras

Mathematics Subject Classification ID

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 (20)

Graded polynomial identities as identities of universal algebras ⋮ Verbally prime T-ideals and graded division algebras ⋮ Minimal varieties of associative PI (super)-algebras with respect to their (graded) exponent ⋮ Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras. ⋮ Graded polynomial identities on upper block triangular matrix algebras. ⋮ Varieties of group graded algebras with graded involution of almost polynomial growth ⋮ The isomorphism problem in the context of PI-theory for two-dimensional Jordan algebras ⋮ On some minimal supervarieties of exponential growth. ⋮ Graded embeddings of finite dimensional simple graded algebras. ⋮ Graded identities of simple real graded division algebras ⋮ On the utility of Robinson-Amitsur ultrafilters ⋮ Graded identities and isomorphisms on algebras of upper block-triangular matrices ⋮ On some \(H\)-Galois objects and their polynomial \(H\)-identities ⋮ Identities and isomorphisms of finite-dimensional graded simple algebras ⋮ Simple 𝐺-graded algebras and their polynomial identities ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Polynomial Identities of Finite Dimensional Simple Algebras ⋮ Distinguishing simple algebras by means of polynomial identities ⋮ Group Gradings on Finite Dimensional Lie Algebras ⋮ On the minimal varieties of PI-algebras graded by finite cyclic groups

Cites Work

• Polynomial identities for graded tensor products of algebras.
• Polynomial identities and nonidentities of split Jordan pairs
• Graded identities of matrix algebras and the universal graded algebra
• Distinguishing simple jordan algebras by means of polynomial identities
• Group Gradings on Matrix Algebras
• Finite-dimensional simple graded algebras
• Group gradings on associative algebras
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