; a ∈ A,m ∈ M, b ∈ B} equipped with the usual 2× 2 matrix-like addition and matrix-like multiplication is an algebra. An algebra T is called a triangular algebra if there exist algebras A and B and nonzero A−B-bimodule M such that T is (algebraically) isomorphic to Tri(A,M,B) under matrixlike addition and matrix-like multiplication; cf. [1]. For example, the algebra Tn of n × n upper triangular...

As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...

For the quantum group GLp,q(2) and the corresponding quantum algebra Up,q(gl(2)) Fronsdal and Galindo [1] explicitly constructed the so-called universal T -matrix. In a previous paper [2] we showed how this universal T -matrix can be used to exponentiate representations from the quantum algebra to get representations (left comodules) for the quantum group. Here, further properties of the univer...

Based on the tetrahedral Zamolodchikov algebra, we prove the Yang-Baxter equation for the R-matrix of 1-D SU(n) Hubbard model. Furthermore, we present generalizations of the model. Keyword: Hubbard model, R-matrix, tetralhedral Zamolodchikov algebra