A skew group ring of Z/2Z over U(sl_2), Leonard triples and odd graphs

Ars Mathematica Contemporanea 2026 Open access

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Authors: Hau-Wen Huang, Chin-Yen Lee
DOI: 10.26493/1855-3974.3785.6c4
Cited by: 2

Abstract

We employ a skew group ring of Z/2Z over U(sl₂) to construct modules over the universal Bannai–Ito algebra. Furthermore, we characterize the conditions under which the defining generators act as Leonard triples on these modules. As a combinatorial realization, we establish a surjective algebra homomorphism from the universal Bannai–Ito algebra to the Terwilliger algebra of an odd graph. This homomorphism provides a unified description of Leonard triples on all irreducible modules over the Terwilliger algebra.

Fields of Study & Subjects

Rings Modules and Algebras Algebraic structures and combinatorial models Finite Group Theory Research

Publication details

Journal / source
Ars Mathematica Contemporanea
Publisher
University of Primorska Press
Volume
26
Issue
4
Pages
#P4.04–#P4.04
Publication date
27 January 2026
Language
EN