Affiliation:
1. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Abstract
In this paper, we establish a strong connection between groups and gyrogroups, which provides the machinery for studying gyrogroups via group theory. Specifically, we prove that there is a correspondence between the class of gyrogroups and a class of triples with components being groups and twisted subgroups. This in particular provides a construction of a gyrogroup from a group with an automorphism of order two that satisfies the uniquely 2-divisible property. We then present various examples of such groups, including the general linear groups over [Formula: see text] and [Formula: see text], the Clifford group of a Clifford algebra, the Heisenberg group on a module, and the group of units in a unital C[Formula: see text]-algebra. As a consequence, we derive polar decompositions for the groups mentioned previously.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
9 articles.
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