منابع مشابه
Weight Modules over Exp-polynomial Lie Algebras
In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial “highest weight” has finite dimensional weight spaces. We also get a class of irreducible weight modules with finite dimensional weight spaces over generalized Virasoro algebras which do not occ...
متن کاملKoszul Duality for Modules over Lie Algebras
Let g be a reductive Lie algebra over a field of characteristic zero. Suppose that g acts on a complex of vector spaces M by iλ and Lλ, which satisfy the same identities that contraction and Lie derivative do for differential forms. Out of this data one defines the cohomology of the invariants and the equivariant cohomology of M. We establish Koszul duality between them.
متن کاملWeight Modules of Direct Limit Lie Algebras
In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras A(∞), B(∞), C(∞) and D(∞). Our main tool is the shadow method introduced recently in [DMP]. The integrable irreducible modules are an important particular class and we give an explicit parametrization of the finite integrable m...
متن کاملWhittaker Modules for Graded Lie Algebras
In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a consequence of this, we obtain a c...
متن کاملOn Lie Algebras in the Category of Yetter - Drinfeld Modules
The category of Yetter-Drinfeld modules YD K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K such that the set of primitive elements P (H) is a Lie algebra in this sense...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1981
ISSN: 0018-2079
DOI: 10.32917/hmj/1206134102