The $S_4$-action on the Tetrahedron algebra

Abstract

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.

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