Result: Some twisted results

Title:
Some twisted results
Authors:
Gould, MD, Lekatsas, T
Contributors:
C Bender
Source:
Journal of Physics A: Mathematical and General. 38:10123-10144
Publication Status:
Preprint
Publisher Information:
IOP Publishing, 2005.
Publication Year:
2005
Subject Terms:
Operator algebra methods applied to problems in quantum theory, Multidisciplinary, Quasi-hopf Superalgebras, Mathematical, 81R50, 16W30, Physics, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Mathematical Physics (math-ph), Algebras, 01 natural sciences, Hopf algebras (associative rings and algebras), 780101 Mathematical sciences, C1, 230199 Mathematics not elsewhere classified, Mathematics - Quantum Algebra, Elliptic Quantum Groups, FOS: Mathematics, Quantum Algebra (math.QA), 0101 mathematics, Quantum groups and related algebraic methods applied to problems in quantum theory, Mathematical Physics
Document Type:
Academic journal Article<br />Other literature type
File Description:
application/xml
ISSN:
1361-6447
0305-4470
DOI:
10.1088/0305-4470/38/47/006
DOI:
10.48550/arxiv.math/0504184
Access URL:
http://arxiv.org/abs/math/0504184
https://core.ac.uk/display/15010405
https://espace.library.uq.edu.au/view/UQ:77526
https://inis.iaea.org/Search/search.aspx?orig_q=RN:37048546
http://ui.adsabs.harvard.edu/abs/2005JPhA...3810123G/abstract
https://arxiv.org/abs/math/0504184
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....9777dcb41797bbefa7525bea291710b0
Database:
OpenAIRE

Further Information

The Drinfeld twist for the opposite quasi-Hopf algebra is determined and is shown to be related to the (second) Drinfeld twist. The twisted Drinfeld twist is investigated. In the quasi-triangular case it is shown that the Drinfeld u operator arises from the equivalence of the opposite quasi-Hopf algebra to the quasi-Hopf algebra induced by twisting with the R-matrix. The Altschuler-Coste u operator arises in a similar way and is shown to be closely related to the Drinfeld u operator. The quasi-cocycle condition is introduced, and is shown to play a central role in the uniqueness of twisted structures on quasi-Hopf algebras. A generalisation of the dynamical quantum Yang-Baxter equation, called the quasi-dynamical quantum Yang-Baxter equation is introduced.
26 pages