Journal of Nonlinear Mathematical Physics

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Volume 16, Issue 1, March 2009, Pages 63 - 75

The Adjoint Representation of Quantum Algebra Uq(sl(2))

Authors
Č. Burdík*, ‡, O. Navrátil†, §, S. Pošta*,
*Department of Mathematics, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Czech Republic
†Department of Mathematics, Czech Technical University, Faculty of Transportation Sciences, Czech Republic
Received 9 February 2008, Accepted 2 April 2008, Available Online 7 January 2021.
DOI
10.1142/S1402925109000066How to use a DOI?
Keywords
Quantum algebra; enveloping algebra; adjoint representation
Abstract

Starting from any representation of the Lie algebra ℊ on the finite dimensional vector space V we can construct the representation on the space Aut(V ). These representations are of the type of ad. That is one of the reasons, why it is important to study the adjoint representation of the Lie algebra ℊ on the universal enveloping algebra U(g). A similar situation is for the quantum groups Uq(ℊ). In this paper, we study the adjoint representation for the simplest quantum algebra Uq(sl(2)) in the case that q is not a root of unity.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 1
Pages
63 - 75
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925109000066How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Č. Burdík
AU  - O. Navrátil
AU  - S. Pošta
PY  - 2021
DA  - 2021/01/07
TI  - The Adjoint Representation of Quantum Algebra Uq(sl(2))
JO  - Journal of Nonlinear Mathematical Physics
SP  - 63
EP  - 75
VL  - 16
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000066
DO  - 10.1142/S1402925109000066
ID  - Burdík2021
ER  -