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Mathematics 2006
The $S_4$-action on the Tetrahedron algebraAbstract: The action of the symmetric group of degree 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.
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