Gradings on the algebra of upper triangular matrices and their graded identities.

DOI10.1016/j.jalgebra.2003.08.004zbMath1066.16047OpenAlexW2002128103MaRDI QIDQ1883027

Angela Valenti, Plamen Koshlukov, Onofrio Mario di Vincenzo

Publication date: 1 October 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.08.004

zbMATH Keywords

T-idealsgraded identitiesupper triangular matriceselementary gradingsrelatively free graded 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) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (47)

Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3 ⋮ On the *-Polynomial Identities of a Class of *-Minimal Algebras ⋮ Homogeneous involutions on upper triangular matrices ⋮ \(\mathbb{Z}_2\)-graded cocharacters for superalgebras of triangular matrices. ⋮ Graded polynomial identities as identities of universal algebras ⋮ Identities with involution for \(2\times 2\) upper triangular matrices algebra over a finite field ⋮ Automorphisms and superalgebra structures on the Grassmann algebra ⋮ Involutions for upper triangular matrix algebras. ⋮ \(\mathbb{Z}\)-graded polynomial identities of the Grassmann algebra ⋮ Cocharacters of group graded algebras and multiplicities bounded by one ⋮ Minimal varieties of associative PI (super)-algebras with respect to their (graded) exponent ⋮ Degree-inverting involution on full square and triangular matrices ⋮ Gradings on incidence algebras and their graded polynomial identities ⋮ Group gradings on the Jordan algebra of upper triangular matrices ⋮ On ℤ_n-graded identities of block-triangular matrices ⋮ Gradings on the algebra of upper triangular matrices of size three. ⋮ On \(\mathbb Z_2\)-graded identities of the generalized Grassmann envelope of the upper triangular matrices \(UT_{k,l}(F)\). ⋮ Graded polynomial identities for the upper triangular matrix algebra over a finite field ⋮ Graded polynomial identities on upper block triangular matrix algebras. ⋮ Images of multilinear graded polynomials on upper triangular matrix algebras ⋮ Gradings on block-triangular matrix algebras ⋮ Group gradings on the Lie and Jordan algebras of upper triangular matrices ⋮ \(Y\)-proper graded cocharacters of the algebra \(UT_m(F)\) of \(m \times m\) upper triangular matrices over \(F\) ⋮ Actions of Taft's algebras on finite dimensional algebras ⋮ Graded identities with involution for the algebra of upper triangular matrices ⋮ A Lie algebra over a finite field of characteristic 2: graded polynomial identities and Specht property ⋮ On some minimal supervarieties of exponential growth. ⋮ Group graded algebras and multiplicities bounded by a constant. ⋮ \(Y\)-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4. ⋮ Asymptotics of graded codimension of upper triangular matrices ⋮ Upper triangular matrices of graded division algebras and their identities ⋮ On the combinatorics of commutators of Lie algebras ⋮ Superinvolutions on upper-triangular matrix algebras ⋮ Elementary gradings on the Lie algebra \(UT_n^{(-)}\) ⋮ Group gradings on the Lie algebra of upper triangular matrices ⋮ Distinguishing simple algebras by means of polynomial identities ⋮ \(Y\)-proper graded cocharacters of upper triangular matrices of order \(m\) graded by the \(m\)-tuple \(\phi=(0,0,1,\ldots,m-2)\). ⋮ On \(\mathbb Z_2\)-graded identities of the super tensor product of \(UT_2(F)\) by the Grassmann algebra. ⋮ On \(\mathbb Z_2\)-graded identities of \(UT_2(E)\) and their growth. ⋮ Identities of *-superalgebras and almost polynomial growth ⋮ On the number of gradings on matrix algebras ⋮ Graded identities of block-triangular matrices ⋮ Identities of PI-Algebras Graded by a Finite Abelian Group ⋮ Classifying good gradings on structural matrix algebras ⋮ A NOTE ON GRADED GELFAND–KIRILLOV DIMENSION OF GRADED ALGEBRAS ⋮ Group gradings on finite dimensional incidence algebras ⋮ Good Gradings on Upper Block Triangular Matrix Algebras

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