Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T09:11:09.788Z Has data issue: false hasContentIssue false

Quantizations of the Module of Tensor Fields Over the Witt Algebra

Published online by Cambridge University Press:  20 November 2018

Ke-Qin Liu*
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2GJ
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

After introducing the q-analogue of the enveloping algebra of the Witt algebra, we construct q-analogues of the module of tensor fields over the Witt algebra and prove a partial q-analogue of Kaplansky's Theorem concerning this module of tensor fields.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Feigin, B. L. and Fuchs, D. B., Invariant skew-symmetric differential operator on the line and Verma modules over the Virasoro algebra, Funct. Anal. Appl. (English translation) 16(1982), 114126.Google Scholar
2. Kac, V. G. and Raina, A. K., Highest weight representations of infinite dimensional Lie algebras, World Scientific Publishing Co. Pte. Ltd., 1987. 3.1. Kaplansky, The Virasoro algebra, Commun. Math. Phys. 86(1982), 4954.Google Scholar
4. Kaplansky, I. and Santharoubane, L. J., Harish-Chandra modules over the Virasoro algebra, Proc. Conf. Infinite Dimensional Lie groups, Publications MSRI.Google Scholar
5. Liu, K. Q., Quantum central extensions, C. R. Math. Rep. Acad. Sci. Canada (4) XIII(1991), 135140.Google Scholar
6. Moody, R. V. and Pianzola, A., Lie algebras with triangular decomposition, preprint.Google Scholar