The half-twist for U_q(g) representations

Abstract

We introduce the notion of a half-ribbon Hopf algebra, which is a ribbon Hopf algebra along with a distinguished element $t$ 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.

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

References in corpus (1)

• The crystal commutor and Drinfeld's unitarized R-matrix

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