Decomposition of quandle rings of Takasaki quandles

Abstract

Let $K=\mathbb{R}$ or $\mathbb{C}$ and $T_n$ denote the Takasaki quandle of order $n$. In this article we provide decomposition of quandle ring $K[T_n]$ as direct sum of right simple ideals. This decomposition is equivalent to decomposition of regular representation \cite{EM18} of Takasaki quandles.

14 pages