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The $S_4$-action on tetrahedron algebra

Published online by Cambridge University Press:  03 December 2007

Alberto Elduque
Alberto Elduque
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain ([email protected])
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Abstract

The action of the symmetric group $S_4$ on the tetrahedron algebra, introduced by Hartwig and Terwilliger, is studied. This action gives a grading of the algebra which is related to its decomposition into a direct sum of three subalgebras isomorphic to the Onsager algebra. The ideals of both the tetrahedron algebra and the Onsager algebra are determined.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 6 , December 2007 , pp. 1227 - 1248
Copyright
2007 Royal Society of Edinburgh

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