RESEARCH ARTICLE

Whittaker modules for a Lie algebra of Block type

  • Bin WANG 1 ,
  • Xinyun ZHU , 2
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  • 1. Department of Mathematics, Changshu Institute of Technology, Changshu 215500, China
  • 2. Department of Mathematics, University of Texas of the Permian Basin, Odessa, TX79762, USA

Received date: 06 Sep 2010

Accepted date: 16 Mar 2011

Published date: 01 Aug 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

In this paper, we study Whittaker modules for a Lie algebra of Block type. We define Whittaker modules and under some conditions, obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules over this algebra and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra.

Cite this article

Bin WANG , Xinyun ZHU . Whittaker modules for a Lie algebra of Block type[J]. Frontiers of Mathematics in China, 2011 , 6(4) : 731 -744 . DOI: 10.1007/s11464-011-0121-1

1
Benkart G, Ondrus M. Whittaker modules for Generalized Weyl algebras. Represent Theory, 2009, 13: 141-164

DOI

2
Christodoulopoulou K. Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras. J Algebra, 2008, 320: 2871-2890

DOI

3
Dokovic D, Zhao K. Derivations, isomorphisms and cohomology of generalized Block algebras. Algebra Colloq, 1996, 3: 245-272

4
Kostant B. On Whittaker vectors and representation theory. Invent Math, 1978, 48: 101-184

DOI

5
Lin W, Tan S. Nonzero level Harish-Chandra modules over the Virasoro-like algebra. J Pure Appl Algebra, 2006, 204: 90-105

DOI

6
Ondrus M. Whittaker modules for Uq(sl2). J Algebra, 2005, 289: 192-213

DOI

7
Ondrus M, Wiesenr E. Whittaker modules for the Virasoro algebra. J Algebra Appl, 2009, 8: 363-377

DOI

8
Sevostyanov A. Quantum deformation of Whittaker modules and Toda lattice. Duke Math J, 2000, 204: 211-238

DOI

9
Su Y. Quasifinite representations of a Lie algebra of Block type. J Algebra, 2004, 276: 117-128

DOI

10
Su Y. Quasifinite representations of a family of Lie algebras of Block type. J Pure Appl Algebra, 2004, 192: 293-305

DOI

11
Wang B. Whittaker Modules for graded Lie algebras. Algebras and the Representation Theory (to appear); arXiv: 0902.3801

12
Wu Y, Su Y. Highest weight representations of a Lie algebra of Block type. Sci China, Ser A, 2007, 50: 1267-1279

DOI

13
Xu X. Generalizations of Block algebras. Manuscripta Math, 1999, 100: 489-518

DOI

14
Xu X. Quadratic conformal superalgebras. J Algebra, 2000, 231: 1-38

DOI

15
Yue X, Su Y. Classification of ℤ2-graded modules of the intermediate series over a Lie algebra of Block type. arXiv.math/0611942v2

16
Zhang H, Zhao K. Representations of the Virasoro-like Lie algebra and its q-analog. Commun Algebra, 1996, 24: 4361-4372

DOI

17
Zhang X, Tan S, Lian H. Whittaker modules for the Schrödinger-Witt algebra. J Math Phys, 2010, 51: 083524

DOI

18
Zhu L, Meng D. Structure of degenerate Block algebras. Algebra Colloq, 2003, 10: 53-62

DOI

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