On Z-graded associative algebras and their N-graded modules
نویسندگان
چکیده
Let A be a Z-graded associative algebra and let ρ be an irreducible N-graded representation of A on W with finite-dimensional homogeneous subspaces. Then it is proved that ρ(Ã) = glJ (W ), where à is the completion of A with respect to a certain topology and glJ (W ) is the subalgebra of EndW , generated by homogeneous endomorphisms. It is also proved that an N-graded vector space W with finite-dimensional homogeneous spaces is the only continuous irreducible N-graded glJ(W )-module up to equivalence, where glJ (W ) is considered as a topological algebra in a certain natural way, and that any continuous N-graded glJ (W )-module is a direct sum of some copies of W . A duality for certain subalgebras of glJ (W ) is also obtained.
منابع مشابه
Research Statement Oleg N. Smirnov
1.1 Graded associative algebras. A nite Z-grading of an algebra A is a decomposition A = L n i=?n A i such that A i A j A i+j , where A i = 0 for jij > n. From now on a grading means a nite Z-grading. I am interested in associative graded algebras because they arise naturally in study of Lie algebras, although the subject is certainly interesting in its own right. A classiication of gradings of...
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