The q-tetrahedron algebra and its finite dimensional irreducible modules
نویسندگان
چکیده
Recently B. Hartwig and the second author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation they defined an algebra ⊠ by generators and relations, and displayed an isomorphism from ⊠ to the three-point sl2 loop algebra. We introduce a quantum analog of ⊠ which we call ⊠q. We define ⊠q via generators and relations. We show how ⊠q is related to the quantum group Uq(sl2), the Uq(sl2) loop algebra, and the positive part of Uq(ŝl2). We describe the finite dimensional irreducible ⊠q-modules under the assumption that q is not a root of 1, and the underlying field is algebraically closed.
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