Abstract
Let L be the skew derivation Lie algebra of the quantum torus ℂq. In this paper, we give a class of irreducible representations for L with infinite dimensional weight spaces.
Similar content being viewed by others
References
Berman S, Gao Y, Krylyuk Y S. Quantum tori and the structure of elliptic quasisimple Lie algebras. J Funct Anal, 1996, 135: 339–389
Chen Y, Xue M, Lin W. Structure and automorphism group of a class of derivation Lie algebras over quantum torus. Annals Math, 2005, 26A: 755–764
Eswara Rao S, Jiang C. Classification of irreducible integrable representations for the full toroidal Lie-algebra. J Pure Appl Algebra, 2005, 200: 71–85
Eswara Rao S. A class of integrable modules for the core of EALA coordinatized by quantum tori. J Algebra, 2004, 275: 59–74
Eswara Rao S. Irreducible representations of the Lie-algebra of the diffeomorphisms of a d-dimensional torus. J Algebra, 1996, 182: 401–421
Kirkman E, Procesi C, Small L. A q-analog for the Virasoro algebra. Comm Algebra, 1994, 22: 3755–3774
Larsson T A. Conformal fields: A class of representations of Vcet(N). Internat J Modern Phys A7, 1992, 26: 6493–6508
Lin W, Tan S. Representations of the Lie algebra of derivations for quantum torus. J Algebra, 2004, 275: 250–274
Lin W, Tan S. Representations of the Lie algebra of skew derivations on quantum torus. Adv Math, 2005, 34: 477–489
Lin W, Tan S. Central extension and derivations of the Lie algebras of skew derivations for the quantum torus. Comm Algebras, 2005, 11: 3919–3938
Lin W, Tan S. Nonzero level Harish-Chandra modules over the Virasoro-like algebra. J Pure Appl Algebra, 2006, 204: 90–105
Lin W, Tan S. Harish-Chandra modules for the q-analog Virasoro-like algebra. J Algebra, 2006, 297: 254–272
Shen G. Graded modules of graded Lie algebras of Cartan type (I). Scientia Sinica A, 1986, 29(6): 570–581
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, N. Class of representations of skew derivation Lie algebra over quantum torus. Front. Math. China 3, 119–131 (2008). https://doi.org/10.1007/s11464-008-0003-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11464-008-0003-3