scholarly journals WEAK HOPF ALGEBRAS CORRESPONDING TO NON-STANDARD QUANTUM GROUPS

2017 ◽  
Vol 54 (2) ◽  
pp. 463-484 ◽  
Author(s):  
Cheng Cheng ◽  
Shilin Yang
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Standard Quantum ◽  
Weak Hopf Algebras

scholarly journals A CLOSED EXPRESSION FOR THE UNIVERSAL ℛ-MATRIX IN A NON-STANDARD QUANTUM DOUBLE

1993 ◽  
Vol 08 (27) ◽  
pp. 2573-2578 ◽  
Author(s):  
A.A. VLADIMIROV
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Reduced Form ◽  
Elementary Functions ◽  
Quantum Double ◽  
Closed Expression ◽  
Standard Quantum ◽  
Number Of Generators

In recent papers by the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In this letter, a closed expression (in terms of elementary functions) for the corresponding universal ℛ-matrix is obtained. In reduced form, when the number of generators becomes two instead of four, this quantum group can be interpreted as a deformation of the Lie algebra [x, h]=2h in the context of Drinfeld’s quantization program.

scholarly journals Crossed products for weak Hopf algebras with coalgebra splitting

2004 ◽  
Vol 281 (2) ◽  
pp. 731-752 ◽  
Author(s):  
J.N. Alonso Álvarez ◽  
R. González Rodríguez
Keyword(s):  
Hopf Algebras ◽  
Crossed Products ◽  
Weak Hopf Algebras

A braided T-category over weak monoidal Hom-Hopf algebras

2019 ◽  
Vol 19 (08) ◽  
pp. 2050159
Author(s):  
Guohua Liu ◽  
Wei Wang ◽  
Shuanhong Wang ◽  
Xiaohui Zhang
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Weak Hopf Algebras ◽  
T Category

In this paper, we define and study weak monoidal Hom-Hopf algebras, which generalize both weak Hopf algebras and monoidal Hom-Hopf algebras. Let [Formula: see text] be a weak monoidal Hom-Hopf algebra with bijective antipode and let [Formula: see text] be the set of all automorphisms of [Formula: see text], we introduce a category [Formula: see text] with [Formula: see text] and construct a braided [Formula: see text]-category [Formula: see text] having all the categories [Formula: see text] as components.

scholarly journals Doi-hopf modules over weak hopf algebras

2000 ◽  
Vol 28 (10) ◽  
pp. 4687-4698 ◽  
Author(s):  
Gabriella Böhm
Keyword(s):  
Hopf Algebras ◽  
Hopf Modules ◽  
Weak Hopf Algebras

scholarly journals INTRODUCTION TO QUANTIZED LIE GROUPS AND ALGEBRAS

1992 ◽  
Vol 07 (25) ◽  
pp. 6175-6213 ◽  
Author(s):  
T. TJIN
Keyword(s):  
Lie Groups ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Baxter Equation ◽  
Product Decomposition ◽  
R Matrix ◽  
Conformal Field ◽  
Finite Dimensional ◽  
Lie Groups And Algebras ◽  
Poisson Lie Groups

We give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups we study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then we explain in detail the concept of quantization for them. As an example the quantization of sl2 is explicitly carried out. Next we show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction we explicitly construct the universal R matrix for the quantum sl2 algebra. In the last section we deduce all finite-dimensional irreducible representations for q a root of unity. We also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.

Sign in / Sign up

Export Citation Format

Share Document