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https://hdl.handle.net/10316/4660
Title: | Quasialgebra Structure of the Octonions | Authors: | Albuquerque, Helena Majid, Shahn |
Issue Date: | 1999 | Citation: | Journal of Algebra. 220:1 (1999) 188-224 | Abstract: | We show that the octonions are a twisting of the group algebra of 2 × 2 × 2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. In particular, we show that they are quasialgebras associative up to a 3-cocycle isomorphism. We show that one may make general constructions for quasialgebras exactly along the lines of the associative theory, including quasilinear algebra, representation theory, and an automorphism quasi-Hopf algebra. We study the algebraic properties of quasialgebras of the type which includes the octonions. Further examples include the higher 2n-onion Cayley algebras and examples associated to Hadamard matrices. | URI: | https://hdl.handle.net/10316/4660 | DOI: | 10.1006/jabr.1998.7850 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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