Decomposition of quandle rings of dihedral quandles

Dilpreet Kaur () and Pushpendra Singh
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Dilpreet Kaur: Indian Institute of Technology Jodhpur
Pushpendra Singh: Indian Institute of Technology Jodhpur

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 726-730

Abstract: Abstract Let $$K = {\mathbb {R}}$$ K = R or $${\mathbb {C}}$$ C and $${\mathcal {R}}_n$$ R n be the dihedral quandle of order n. In this article, we give decomposition of the quandle ring $$K[{\mathcal {R}}_n]$$ K [ R n ] into indecomposable right $$K[{\mathcal {R}}_n]$$ K [ R n ] -modules for all even $$n \in {\mathbb {N}}$$ n ∈ N . It follows that the decomposition of $$K[{\mathcal {R}}_n]$$ K [ R n ] given in [2, Prop. 4.18(2)] is valid only in the case when n is not divisible by 4.

Keywords: Quandle rings; Dihedral quandles; Dihedral groups; Representations and characters (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00405-2

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