منابع مشابه
Group Actions on Central Simple Algebras
Let G be a group, F a field, and A a finite-dimensional central simple algebra over F on which G acts by F -algebra automorphisms. We study the ideals and subalgebras of A which are preserved by the group action. Let V be the unique simple module of A. We show that V is a projective representation of G and A = EndD(V ) makes V into a projective representation. We then prove that there is a natu...
متن کاملLie Group Actions on Simple Algebras
Let G be a connected Lie group acting by algebra automorphisms on a finite-dimensional complex central simple algebra A. The algebra A is isomorphic to the endomorphism algebra of a projective representation V of G. We study the invariant subalgebras of A. In particular, we show that if V is irreducible, then the invariant subalgebras appear in dual pairs arising from factorizations of V . We a...
متن کاملOn Equivalences between Blocks of Group Algebras: Reduction to the Simple Components
A conjecture of Michel Brou e states that if D is an abelian Sylow p-subgroup of a nite group G, and H = N G (D), then the principal blocks of G and H are Rickard equivalent. The structure of groups with abelian Sylow p-subgroups, as determined by P. Fong and M.E. Harris, raises the following question: assuming that Brou e's conjecture holds for the simple components of G, under what conditions...
متن کاملGroup Gradings on Simple Lie Algebras in Positive Characteristic
In this paper we describe all gradings by a finite abelian group G on the following Lie algebras over an algebraically closed field F of characteristic p = 2: sln(F ) (n not divisible by p), son(F ) (n ≥ 5, n = 8) and spn(F ) (n ≥ 6, n even).
متن کاملSome result on simple hyper K-algebras
A simple method is described, to prove some theorems for simple hyper K-algebras and to study positive implicative hyper K-ideals, weak (implicative ) hyper K-ideals in simple hyper K-algebras . Beside, some results on positive implicative and (weak) implicative simple hyper K-algebras are presented. Finally classification of simple hyper Kalgebras of order 4, which are satisfied in conditions ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1983
ISSN: 0021-8693
DOI: 10.1016/0021-8693(83)90135-7