GROUP GRADINGS ON FINITARY SIMPLE LIE ALGEBRAS
نویسندگان
چکیده
منابع مشابه
Gradings on simple algebras of finitary matrices
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
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The fine abelian group gradings on the simple classical Lie algebras (including D4) over algebraically closed fields of characteristic 0 are determined up to equivalence. This is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them.
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Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
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2 Kac coordinates 5 2.1 Based automorphisms and affine root systems . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Torsion points, Kac coordinates and the normalization algorithm . . . . . . . . . . . . 9 2.3 μm-actions on Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Principal μm-actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2012
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196712500464