New R-matrices for Small Quantum Groups

It is widely accepted that small quantum groups should possess a quasitriangular structure, even though this is technically not true. In this article we construct explicit R -matrices, sometimes several inequivalent ones, over certain natural extensions of small quantum groups by grouplike elements....

Full description

Saved in:
Bibliographic Details
Published inAlgebras and representation theory Vol. 18; no. 6; pp. 1649 - 1673
Main Authors Lentner, Simon, Nett, Daniel
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2015
Subjects
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
16T05
Quantum group
R-matrix
Braided category
Online AccessGet full text

Cover

More Information
Summary:It is widely accepted that small quantum groups should possess a quasitriangular structure, even though this is technically not true. In this article we construct explicit R -matrices, sometimes several inequivalent ones, over certain natural extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice. Our result generalizes a well-known calculation for u q (𝔰𝔩 2 ) used in logarithmic conformal field theories.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-015-9555-6