Division algebras in linear Gr-categories

被引：0

作者：

Huang, Hua-Lin ^{[1
]}

Van Oystaeyen, Fred ^{[2
]}

Zhang, Yinhuo ^{[3
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium

[3] Univ Hasselt, Dept Math & Stat, B-3590 Diepenbeek, Belgium

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2014年 / 21卷 / 05期

关键词：

division algebra; group cohomology; Gr-category;

D O I：

10.36045/bbms/1420071858

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：859 / 872

页数：14

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