Graded polynomial identities of matrices
By Yuri A. Bahturin, V. Drensky. 2002
87 citations recorded by the source corpus.
We consider G-graded polynomial identities of the p×p matrix algebra Mp(K) over a field K of characteristic 0 graded by an arbitrary group G. We find relations between the G-graded identities of the G-graded algebra Mp(K) and the (G×H)-graded identities of the tensor product of Mp(K) and the H-graded algebra Mq(K) with a fine H-grading. We also find a basis of the G-graded identities of Mp(K) with an elementary grading such that the identity component coincides with the diagonal of Mp(K).
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fad12a304b353636abaeca5188f44cafec01aeba
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In Algebra and Number Theory
- Antonio Giambruno
- E. Aljadeff
- D. La Mattina
- Sergey P. Mishchenko
- Mikhail V. Zaicev
- A. Kanel’-Belov
- Alexey Gordienko
- Angela Valenti
In Computational Theory and Mathematics
- E. Aljadeff
- Antonio Giambruno
- D. La Mattina
- Sergey P. Mishchenko
- A. Kanel’-Belov
- Mikhail V. Zaicev
- Alexey Gordienko
In Geometry and Topology
- Antonio Giambruno
- E. Aljadeff
- D. La Mattina
- Mikhail V. Zaicev
- A. Kanel’-Belov
- Alexey Gordienko
- Angela Valenti
- Mikhail Kochetov
Citations in the corpus
- REPRESENTABILITY AND SPECHT PROBLEM FOR G-GRADED ALGEBRAS (2009, background): “Then there exists a field extension K of F and a finite dimensional algebra A over K such that idG(W ) = idG(A).”
- Codimensions of algebras and growth functions (2008, background): “For instance, if dimA = d < ∞, then cn(A) d [3].”
- Graded polynomial identities and codimensions: computing the exponential growth (2010, background): “Such integral scale gives a way to measure the varieties of algebras and it had lead to many results including the classification of the so-called minimal varieties [3,7,13].”