We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a noncocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of the group is achieved by using the adjoint representation. The elements of quantum matrix form a Hopf algebra. Furthermore, we construct a differential calcu...

We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...

Matrix Analysis for Scientists and Engineers provides a blend of undergraduateand graduate-level topics in matrix theory and linear algebra that Laub matrix analysis for a member, of electrical engineering and computer aided control systems society. Degree in numerical linear algebra he joined ucsb as well professor control. Dr the departments of author emphasizes burden society. From the autho...

We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R-matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. These elements are studied...

The technique of computing representations on the enveloping algebra was developed in work by physicists, mainly Gruber (e.g. Gruber and Klimyk (1986)). Their methods are not designed for computations with Lie algebras beyond the simplest ones. Our idea is to construct left and right principal matrices, corresponding to left and right multiplication of the basis elements of the Lie algebra on t...

We consider the double-row (open) transfer matrix constructed from generic representations of various types of Hecke algebras. For different choices of boundary conditions for the relevant integrable lattice model we express the double-row transfer matrix solely in terms of generators of the corresponding Hecke algebra. We then expand the open transfer matrix and extract the associated Murphy e...

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they ...

We classify all decompositions of M3(C) into a direct vector–space sum two subalgebras such that one the contains identity matrix.