Title
Division algebras in linear Gr-categoriesDivision algebras in linear Gr-categories
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
Brussels,
Subject
Mathematics
Source (journal)
Bulletin of the Belgian Mathematical Society Simon Stevin. - Brussels, 1994, currens
Volume/pages
21(2014):5, p. 859-872
ISSN
1370-1444
ISI
000348242800006
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
Abstract
We study division algebras in an arbitrary linear Gr-category, i.e., a category of finite-dimensional vector spaces graded by a group with associativity constraint given by a 3-cocycle. When the 3-cocycle is non-coboundary, this provides some interesting classes of nonassociative division algebras. In particular, when we work on Gr-categories over the field of real numbers, some quasi-associative version of the quaternions and octonions appear.
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