English

The half-twist for U_q(g) representations

Quantum Algebra 2010-10-12 v3 Representation Theory

Abstract

We introduce the notion of a half-ribbon Hopf algebra, which is a ribbon Hopf algebra along with a distinguished element tt corresponding to twisting a ribbon by 180 degrees (the half-twist). We show that U_q(g) is a (topological) half-ribbon Hopf algebra, but only if one uses a modified ribbon element. We then discuss some consequences of using this modified ribbon element.

Keywords

Cite

@article{arxiv.0810.0084,
  title  = {The half-twist for U_q(g) representations},
  author = {Noah Snyder and Peter Tingley},
  journal= {arXiv preprint arXiv:0810.0084},
  year   = {2010}
}

Comments

23 pages. v2: diagrams corrected. v3: Final draft, to appear in Algebra & Number Theory

R2 v1 2026-06-21T11:26:01.428Z