Gyrogroup through its Grothendieck Group Completion and Right gyrogroup action

In this article, we discuss the Grothendieck group completion (GGC) of a gyrogroup. Consequently, we show that there is a one to one correspondence between actions and representations of a gyrogroup, and actions and representations of its Grothendieck group completion. We also introduce the concept...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Kumar, Akshay, Mani Shankar Pandey, Kushwaha, Seema, Upadhyay, Sumit Kumar
Format: Article
Language:English
Subjects:
Representations
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Summary:In this article, we discuss the Grothendieck group completion (GGC) of a gyrogroup. Consequently, we show that there is a one to one correspondence between actions and representations of a gyrogroup, and actions and representations of its Grothendieck group completion. We also introduce the concept of an action of a right gyrogroup.
ISSN:2331-8422