The Tetrahedron algebra and its finite-dimensional irreducible modules

By B. Hartwig. 2006

51 citations recorded by the source corpus.

Abstract Recently Terwilliger and the present author found a presentation for the three-point sl 2 loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ⊠ by generators and relations and displayed an isomorphism from ⊠ to the three-point sl 2 loop algebra. In this paper we classify the finite-dimensional irreducible ⊠-modules.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bca82cb3a729fd83ae65b26eb147f89d1e29a6a5

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In Algebra and Number Theory

1. Tatsuro Ito
2. Paul M. Terwilliger
3. Raimundas Vidunas
4. B. Hartwig

In Geometry and Topology

1. Tatsuro Ito
2. Paul M. Terwilliger
3. Alexei S. Zhedanov
4. Luc Vinet
5. Plamen Iliev
6. 伊藤 達郎

In Statistical and Nonlinear Physics

1. Tatsuro Ito
2. Paul M. Terwilliger

Citations in the corpus

• Finite-Dimensional Irreducible Modules for the Three-Point 𝔰𝔩2 Loop Algebra (2007, background): “He did this by displaying a bijection between (i) the set of isomorphism classes of finite-dimensional irreducible -modules; (ii) the set of isomorphism classes of finite-dimensional irreducible -modules that have type 0 0 (Hartwig, 2007, Theorems 1.7, 1.8).”