; 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...

Two-dimensional exactly solvable loop models, built on the Temperley-Lieb algebra, have previously been introduced to study statistical systems with non-local degrees of freedom such as polymers and percolation. In the continuum scaling limit, these models describe logarithmic minimal Conformal Field Theories (CFTs). In this thesis, we introduce and study new two-dimensional exactly solvable su...

An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-algebras. We show that it is possible to construct a Dirac operator which relates to this filtration in a natural way and which will induce a metric for the weak*-topology on the state space of the algebra. In the particular case of a UHF C*algebra the construction can be made in a way, which relates di...

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