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Verma Modules over Quantum Torus Lie Algebras
- Source :
- Canadian Journal of Mathematics. 62:382-399
- Publication Year :
- 2010
- Publisher :
- Canadian Mathematical Society, 2010.
-
Abstract
- Representations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras . The center of now is generally infinite dimensional.In this paper, Z-graded Verma modules over and their corresponding irreducible highest weight modules are defined for some linear functions . Necessary and sufficient conditions for to have all finite dimensional weight spaces are given. Also necessary and sufficient conditions for Verma modules e to be irreducible are obtained.
- Subjects :
- Pure mathematics
Verma module
General Mathematics
010102 general mathematics
Generalized Verma module
Kac–Moody algebra
01 natural sciences
Affine Lie algebra
Lie conformal algebra
Algebra
Adjoint representation of a Lie algebra
Representation of a Lie group
0103 physical sciences
Maximal torus
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........0912a302ac6177b41c781d88f3f085a1