The $S_4$-action on the Tetrahedron algebra

Details The $S_4$-action on the Tetrahedron algebra The $S_4$-action on the Tetrahedron algebra

2006-04-10

arxiv.org/abs/math/0604218v2

Mathematics

Rings and Algebras

22 pages. Corollary 4.9 has been corrected, as well as some misprints

Scientific paper

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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