Title
Quasi-Hopf algebras and representations of octonions and other quasialgebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Physics
Source (journal)
Journal of mathematical physics. - New York, N.Y.
Volume/pages
45(2004) :10 , p. 3912-3929
ISSN
0022-2488
ISI
000224456600012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Modules over a quasialgebra (here, by quasialgebra we mean a left H-module algebra, where H is a quasi-Hopf algebra), as defined by Albuquerque and Majid, coincide with modules over a certain associative algebra, a quasi-Hopf smash product. As a consequence of this, we get that the category of modules over the octonions is isomorphic to the category of modules over the algebra of 8x8 real matrices. We provide a new approach to the endomorphism quasialgebra associated to a left H-module, which in the finite dimensional case yields the same results as the one of Albuquerque and Majid. We discuss possible definitions as endomorphism quasialgebras for Heisenberg doubles of a finite dimensional quasi-Hopf algebra. (C) 2004 American Institute of Physics.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/6d5dbd/5825.pdf
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