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december 2014 Division algebras in linear Gr-categories
Hua-Lin Huang, Fred Van Oystaeyen, Yinhuo Zhang
Bull. Belg. Math. Soc. Simon Stevin 21(5): 859-872 (december 2014). DOI: 10.36045/bbms/1420071858

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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Hua-Lin Huang. Fred Van Oystaeyen. Yinhuo Zhang. "Division algebras in linear Gr-categories." Bull. Belg. Math. Soc. Simon Stevin 21 (5) 859 - 872, december 2014. https://doi.org/10.36045/bbms/1420071858

Information

Published: december 2014
First available in Project Euclid: 1 January 2015

zbMATH: 06408731
MathSciNet: MR3298482
Digital Object Identifier: 10.36045/bbms/1420071858

Subjects:
Primary: 17A35, 18D10, 20J06

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 5 • december 2014
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