Drinfel'd doubles and Shapovalov determinants
Quantum Algebra
2008-10-10 v1 Representation Theory
Abstract
The Shapovalov determinant for a class of pointed Hopf algebras is calculated, including quantized enveloping algebras, Lusztig's small quantum groups, and quantized Lie superalgebras. Our main tools are root systems, Weyl groupoids, and Lusztig type isomorphisms. We elaborate powerful novel techniques for the algebras at roots of unity, and pass to the general case using a density argument. Key words: Hopf algebra, Nichols algebra, quantum group, representation
Cite
@article{arxiv.0810.1621,
title = {Drinfel'd doubles and Shapovalov determinants},
author = {I. Heckenberger and H. Yamane},
journal= {arXiv preprint arXiv:0810.1621},
year = {2008}
}
Comments
50 pages