Noah Snyder And
نویسنده
چکیده
We introduce the notion of a half-ribbon Hopf algebra, which is a Hopf algebra H along with a distinguished element t ∈ H such that (H, R,C) is a ribbon Hopf algebra, where R = (t ⊗ t)∆(t) and C = t. The element t is closely related to the topological ‘half-twist’, which twists a ribbon by 180 degrees. We construct a functor from a topological category of ribbons with half-twists to the category of representations of any half-ribbon Hopf algebra. We show that Uq(g) is a (topological) half-ribbon Hopf algebra, but that t −2 is not the standard ribbon element. For Uq(sl2), we show that there is no half-ribbon element t such that t is the standard ribbon element. We then discuss how ribbon elements can be modified, and some consequences of these modifications.
منابع مشابه
Noah Snyder : Teaching Statement
I have long enjoyed teaching, and have had a wide variety of teaching jobs over the past dozen years. I’ve worked in many different capacities at summer math programs for nine summers, I taught a sophomore tutorial at Harvard, I’ve given over 30 seminar talks at Berkeley, and I taught four sections of Calculus at U.C. Berkeley. Beyond a general interest in teaching, I have strong particular int...
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