scholarly journals Differential Hopf Algebras on Quantum Groups of Type A

1999 ◽  
Vol 214 (2) ◽  
pp. 479-518 ◽  
Author(s):  
Axel Schüler
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Type A

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

scholarly journals PBW-type filtration on quantum groups of type A

2016 ◽  
Vol 449 ◽  
pp. 321-345 ◽  
Author(s):  
Xin Fang ◽  
Ghislain Fourier ◽  
Markus Reineke
Keyword(s):  
Quantum Groups ◽  
Type A

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.

scholarly journals Multi-brace cotensor Hopf algebras and quantum groups

2016 ◽  
Vol 286 (1-2) ◽  
pp. 657-678
Author(s):  
Xin Fang ◽  
Marc Rosso
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras

scholarly journals Quantum groups and conformal field theories

1989 ◽  
Vol 329 (1605) ◽  
pp. 343-347
Keyword(s):  
Hopf Algebra ◽  
Quantum Groups ◽  
Hopf Algebras ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Theory ◽  
Conformal Field

Rational conformal field theories can be interpreted as defining quasi-triangular Hopf algebras. The Hopf algebra is determined by the duality properties of the conformal theory.

scholarly journals Two Maps on Affine Type $A$ Crystals and Hecke Algebras

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Nicolas Jacon
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
Fock Space ◽  
Hecke Algebras ◽  
Type A ◽  
Crystal Basis ◽  
Affine Type

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type $A$ and in the representation theory of Hecke algebras of type $G(l,l,n)$. 

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