Decomposition of quandle rings of Takasaki quandles

ISSN
02194988
Date Issued
2023-01-01
Author(s)
Kaur, Dilpreet
Singh, Pushpendra
DOI
10.1142/S0219498825500227
Abstract
Let K = R or C and Tn denote the Takasaki quandle of order n. In this paper, we provide decomposition of quandle ring K[Tn] as direct sum of right simple ideals. This decomposition is equivalent to decomposition of regular representation [M. Elhamdadi and E. M. Moutuou, Finitely stable racks and rack representations, Comm. Algebra 46(11) (2018) 4787-4802] of Takasaki quandles.
Subjects