Graded central polynomials for the matrix algebra of order two

Brandão, Antônio Pereira; Koshlukov, Plamen; Krasilnikov, Alexei

doi:10.1007/s00605-008-0046-2

Cited by 7 publications

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References 13 publications

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“…Also the Lie and Jordan analogues for some relatively easy results in the associative case either are not true or if true they are much more intricate to obtain. We refer the interested reader to compare the description of the graded identities for the associative algebra M 2 (K ) (done in [10] in characteristic 0, in [1] in positive characteristic different from 2, and finally in [9] when the algebra is over an infinite integral domain instead of a field) on one hand, and the Lie analogue given in [18]. While the former takes at most half a page and it is quite elementary the latter occupies more than 10 pages and applies methods from Invariant theory.…”

Section: Introductionmentioning

confidence: 99%

Group gradings on the Lie and Jordan algebras of upper triangular matrices

Hitomi

Koshlukov

Yasumura

2017

São Paulo J. Math. Sci.

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Let K be a field and let U T n = U T n (K) denote the associative algebra of upper triangular n × n matrices over K. The vector space of U T n can be given the structure of a Lie and of a Jordan algebra, respectively, by means of the new products: [a, b] = ab − ba, and a • b = ab + ba. We denote the corresponding Lie and Jordan algebra by U T − n and by U T + n , respectively. If G is a group, the G-gradings on U T n were described by Valenti and Zaicev (Arch Math 89(1):33-40, 2007); they proved that each grading on U T n is isomorphic to an elementary grading (that is every matrix unit is homogeneous). Also Di Vincenzo et al. (J Algebra 275(2):550-566, 2004) classified all elementary gradings on U T n. Here we study the gradings and the graded identities on U T − n and on U T +

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Section: Introductionmentioning

confidence: 99%

Group gradings on the Lie and Jordan algebras of upper triangular matrices

Hitomi

Koshlukov

Yasumura

2017

São Paulo J. Math. Sci.

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“…Moreover in [4] the Z 2 -graded central polynomials for M 2 (K) were described when K is an infinite integral domain.…”

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confidence: 99%

Graded central polynomials for the algebra M n (K)

Brandão

2008

Rend. Circ. Mat. Palermo

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Graded polynomial identities and central polynomials of matrices over an infinite integral domain

Fonseca

2014

Rend. Circ. Mat. Palermo

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Let K be an infinite integral domain and M n (K ) be the algebra of all n ×n matrices over K . This paper aims for the following goals:• Find a basis for the graded identities for elementary grading in M n (K ) when the neutral component and diagonal coincide; • Describe the Z p -graded central polynomials of M p (K ) when p is a prime number;• Describe the Z-graded central polynomials of M n (K ).

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Graded central polynomials for the matrix algebra of order two

Cited by 7 publications

References 13 publications

Group gradings on the Lie and Jordan algebras of upper triangular matrices

Group gradings on the Lie and Jordan algebras of upper triangular matrices

Graded central polynomials for the algebra M n (K)

Graded polynomial identities and central polynomials of matrices over an infinite integral domain

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