Group Gradings on Matrix Algebras

By Yuri A. Bahturin, Mikhail V. Zaicev. Canadian mathematical bulletin, 2002

104 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/5522075ff8d246e52ce1dc4354dd446fdfe32da4

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Citations in the corpus

Gradings on simple Jordan and Lie algebras (2005, unknown): “We use these facts in this paper in order to apply our previous results [3] and [2] on the gradings of the full matrix algebras Mn over an algebraically closed field F of characteristic zero to the classification of the gradings by finite Abelian groups for those simple Lie and Jordan algebras which”
Classification of group gradings on simple Lie algebras of types A, B, C and D☆ (2009, background): “A G-grading on U is a vector space decomposition U = ⊕ g∈G Ug such that UgUh ⊂ Ugh for all g, h ∈ G. Ug is called the homogeneous component of degree g.”
Algebraic quantum permutation groups (2007, background): “It is worthwhile to note that the classification problem for group gradings over various classes of associative algebras (matrix algebras, triangular algebras, incidence algebras...) has been intensively studied in recent years: see [1, 16, 15].”
Group gradings on upper triangular matrices (2007, background): “for any t = gh ∈ T. Then (4) defines a T -grading on A ⊗ B. More generally, if T is any group and G and H are subgroups of T such that the elements of G and H commute in T then (4) can be replaced with (A ⊗ B)t = ⊕gh=tAg ⊗ Bh in order to define a T -grading on A ⊗ B. This construction can be further”
Gradings on the Albert Algebra and on $f_4$ (2007, methodology): “In that work, the authors use their previous results in [9] about gradings of associative algebras Mn(F ).”
Gradings on Finite-Dimensional Simple Lie Algebras (2009, background): “(9) The following result was first obtained in [12] for abelian G and charF = 0, and then extended in [8, 9] to arbitrary G and arbitrary characteristic.”