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- Title
Verma Modules over a Block Lie Algebra.
- Authors
Qifen Jiang; Yuezhu Wu
- Abstract
Let ${\cal B}$ be the Lie algebra with basis {Li,j, C|i, j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - i(l + 1))Li+k, j+l + iδi, -kδj+l, -2C and [C, Li,j] = 0. It is proved that an irreducible highest weight ${\cal B}$-module is quasifinite if and only if it is a proper quotient of a Verma module. An additive subgroup Γ of 픽 corresponds to a Lie algebra ${\cal B}(\Gamma)$ of Block type. Given a total order ≻ on Γ and a weight Λ, a Verma ${\cal B}(\Gamma)$-module M(Λ, ≻) is defined. The irreducibility of M(Λ, ≻) is completely determined.
- Subjects
ALGEBRA; MATHEMATICS; MODULES (Algebra); FINITE groups; MATHEMATICAL analysis
- Publication
Algebra Colloquium, 2008, Vol 15, Issue 2, p235
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386708000230