The homology of Kac-Moody Lie algebras with coefficients in a generalized Verma module
نویسندگان
چکیده
منابع مشابه
6 Generalized Kac - Moody Lie Algebras and Product Quivers
We construct the entire generalized Kac-Moody Lie algebra as a quotient of the positive part of another generalized Kac-Moody Lie algebra. The positive part of a generalized Kac-Moody Lie algebra can be constructed from representations of quivers using Ringel's Hall algebra construction. Thus we give a direct realization of the entire generalized Kac-Moody Lie algebra. This idea arises from the...
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Generalized Kac-Moody algebras can be described in two ways: either using generators and relations, or as Lie algebras with an almost positive definite symmetric contravariant bilinear form. Unfortunately it is usually hard to check either of these conditions for any naturally occurring Lie algebra. In this paper we give a third characterization of generalized Kac-Moody algebras which is easier...
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We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac–Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2 (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fuchs and Malikov [Funct. Anal. Appl. 20 (1986), no. 2, 103–113]. In the simpler case of A1 the for...
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In this paper we consider some algebraic structures associated to a class of outer automorphisms of generalized Kac-Moody (GKM) algebras. These structures have recently been introduced in [2] for a smaller class of outer automorphisms in the case of ordinary Kac-Moody algebras with symmetrizable Cartan matrices. A GKM algebra G = G(A) is essentially described by its Cartan matrix, A = (aij)i,j∈...
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In this paper, we construct new families of graphs whose automorphism groups are transitive on 3-paths. These graphs are constructed from certain Lie algebras related to generalized Kac-Moody algebras of rank two. We will show that one particular subfamily gives new lower bounds on the number of edges in extremal graphs with no cycles of length fourteen.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1984
ISSN: 0021-8693
DOI: 10.1016/0021-8693(84)90194-7