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

共 50 条

[21] Special forms of two symbols are division algebras
Roberto Aravire
Bill Jacob
manuscripta mathematica, 2002, 108 : 139 - 162
[22] Division algebras of prime degree with infinite genus
Sergey V. Tikhonov
Proceedings of the Steklov Institute of Mathematics, 2016, 292 : 256 - 259
[23] SK1 of graded division algebras
R. Hazrat
A. R. Wadsworth
Israel Journal of Mathematics, 2011, 183 : 117 - 163
[24] Decomposition of involutions on inertially split division algebras
Morandi, PJ
Sethuraman, BA
MATHEMATISCHE ZEITSCHRIFT, 2000, 235 (01) : 195 - 212
[25] Supersoluble crossed product criterion for division algebras
R. Ebrahimian
D. Kiani
M. Mahdavi-Hezavehi
Israel Journal of Mathematics, 2005, 145 : 325 - 331
[26] Decomposition of involutions on inertially split division algebras
P.J. Morandi
B.A. Sethuraman
Mathematische Zeitschrift, 2000, 235 : 195 - 212
[27] Galois subfields of inertially split division algebras
Hanke, Timo
JOURNAL OF ALGEBRA, 2011, 346 (01) : 147 - 151
[28] A note on topological divisors of zero and division algebras
J. Carlos Marcos
Ángel Rodríguez-Palacios
M. Victoria Velasco
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2015, 109 : 93 - 100
[29] Division algebras and transitivity of group actions on buildings
Zaremsky, Matthew C. B.
ADVANCES IN GEOMETRY, 2015, 15 (02) : 133 - 142
[30] A note on topological divisors of zero and division algebras
Carlos Marcos, J.
Rodriguez-Palacios, Angel
Victoria Velasco, M.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2015, 109 (01) : 93 - 100

← 1 2 3 4 5 →