Duality for the matrix quantum group GLp,q(2,C)

1992 ◽  
Vol 33 (10) ◽  
pp. 3419-3430 ◽  
Author(s):  
V. K. Dobrev
Keyword(s):  
Quantum Group ◽  
The Matrix ◽  
Matrix Quantum

ON MATRIX QUANTUM GROUPS OF TYPE An

2000 ◽  
Vol 11 (09) ◽  
pp. 1115-1146 ◽  
Author(s):  
HO Hai PHUNG
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Quantum Groups ◽  
Semi Group ◽  
The Matrix ◽  
Hecke Symmetry ◽  
Matrix Quantum

Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend only on the rank of the Hecke symmetry. Further we compute the quantum rank of simple representations. We also show that the quantum semi-group is "Zariski" dense in the quantum group. Finally we give a formula for the integral.

scholarly journals A FINITE QUANTUM SYMMETRY OF $M(3, {\Bbb C})$

1998 ◽  
Vol 13 (24) ◽  
pp. 4147-4161 ◽  
Author(s):  
LUDWIK DABROWSKI ◽  
FABRIZIO NESTI ◽  
PASQUALE SINISCALCO
Keyword(s):  
Standard Model ◽  
Exact Sequence ◽  
Hopf Algebra ◽  
Quantum Group ◽  
Recent Work ◽  
Quantum Groups ◽  
Matrix Algebra ◽  
Group Symmetry ◽  
The Standard Model ◽  
The Matrix

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups [Formula: see text], [Formula: see text], is studied as a finite quantum group symmetry of the matrix algebra [Formula: see text], describing the color sector of Alain Connes' formulation of the Standard Model. The duality with the Hopf algebra ℋ, investigated in a recent work by Robert Coquereaux, is established and used to define a representation of ℋ on [Formula: see text] and two commuting representation of ℋ on A(F).

scholarly journals The dynamicalU(n)quantum group

2006 ◽  
Vol 2006 ◽  
pp. 1-30 ◽  
Author(s):  
Erik Koelink ◽  
Yvette Van Norden
Keyword(s):  
Quantum Group ◽  
Matrix Algebra ◽  
Exterior Algebra ◽  
Matrix Elements ◽  
Algebra Representation ◽  
The Matrix ◽  
Quantum Minor ◽  
Quantum Determinant

We study the dynamical analogue of the matrix algebraM(n), constructed from a dynamicalR-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 in more detail, especially the action of the comultiplication and Laplace expansions. Using the Laplace expansions we can prove that the dynamical quantum determinant is almost central, and adjoining an inverse the antipode can be defined. This results in the dynamicalGL(n)quantum group associated to the dynamicalR-matrix. We study a∗-structure leading to the dynamicalU(n)quantum group, and we obtain results for the canonical pairing arising from theR-matrix.

scholarly journals D-Brane Configurations and Nicolai Map in Supersymmetric Yang–Mills Theory

1997 ◽  
Vol 12 (03) ◽  
pp. 183-193 ◽  
Author(s):  
I. I. Kogan ◽  
R. J. Szabo ◽  
G. W. Semenoff
Keyword(s):  
Quantum Mechanics ◽  
Phase Transitions ◽  
Matrix Model ◽  
Short Distance ◽  
Dimensional Theory ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
M Theory ◽  
Matrix Quantum

We discuss some properties of a supersymmetric matrix model that is the dimensional reduction of supersymmetric Yang–Mills theory in 10 dimensions and which has been recently argued to represent the short-distance structure of M-theory in the infinite momentum frame. We describe a reduced version of the matrix quantum mechanics and derive the Nicolai map of the simplified supersymmetric matrix model. We use this to argue that there are no phase transitions in the large-N limit, and hence that S-duality is preserved in the full 11-dimensional theory.

scholarly journals THE LATTICE QUANTUM PHASE SPACE AND THE YANG-BAXTER EQUATION

1995 ◽  
Vol 10 (23) ◽  
pp. 3303-3318 ◽  
Author(s):  
A.E.F. DJEMAI
Keyword(s):  
Phase Space ◽  
Quantum Group ◽  
Nontrivial Solution ◽  
Symplectic Structure ◽  
Hamiltonian Formalism ◽  
Quantum Phase ◽  
Baxter Equation ◽  
Lattice Quantum ◽  
The Matrix

In this work we show that, in the sense of Ref. 17, it is possible to construct the quantum group which preserves the quantum symplectic structure introduced in the context of the matrix Hamiltonian formalism defined in Ref. 9. We also study the braiding existing behind the lattice quantum phase space, and present another type of nontrivial solution to the resulting Yang-Baxter equation.

scholarly journals The combinatorics of an algebraic class of easy quantum groups

2014 ◽  
Vol 17 (03) ◽  
pp. 1450016 ◽  
Author(s):  
Sven Raum ◽  
Moritz Weber
Keyword(s):  
Symmetric Group ◽  
Quantum Group ◽  
Permutation Group ◽  
Free Product ◽  
Quantum Groups ◽  
Orthogonal Group ◽  
Point Of View ◽  
Algebraic Point ◽  
Matrix Quantum

Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group Sn and the orthogonal group On as well as Wang's quantum permutation group [Formula: see text] and his free orthogonal quantum group [Formula: see text]. In this paper, we study a particular class of categories of partitions to each of which we assign a subgroup of the infinite free product of the cyclic group of order two. This is an important step in the classification of all easy quantum groups and we deduce that there are uncountably many of them. We focus on the combinatorial aspects of this assignment, complementing the quantum algebraic point of view presented in another paper.

scholarly journals Duality for the Jordanian matrix quantum group

1997 ◽  
Vol 30 (19) ◽  
pp. 6769-6781 ◽  
Author(s):  
B L Aneva ◽  
V K Dobrev ◽  
S G Mihov
Keyword(s):  
Quantum Group ◽  
Matrix Quantum
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