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Title
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Quasi-Hopf algebras and representations of octonions and other quasialgebras
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Journal of mathematical physics. - New York, N.Y.
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Publication
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New York, N.Y.
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2004
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ISSN
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0022-2488
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DOI
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10.1063/1.1789280
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Volume/pages
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45
:10
(2004)
, p. 3912-3929
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ISI
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000224456600012
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Full text (Publisher's DOI)
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Full text (open access)
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