441 research outputs found
Comodule Algebras and 2-Cocycles over the (Braided) Drinfeld Double
We show that for dually paired bialgebras, every comodule algebra over one of
the paired bialgebras gives a comodule algebra over their Drinfeld double via a
crossed product construction. These constructions generalize to working with
bialgebra objects in a braided monoidal category of modules over a
quasitriangular Hopf algebra. Hence two ways to provide comodule algebras over
the braided Drinfeld double (the double bosonization) are provided.
Furthermore, a map of second Hopf algebra cohomology spaces is constructed. It
takes a pair of 2-cocycles over dually paired Hopf algebras and produces a
2-cocycle over their Drinfeld double. This construction also has an analogue
for braided Drinfeld doubles.Comment: 34 pages, several figures created with Inkscape. Version 2: more
references added, small typos corrected. Version 3: Small corrections and
further references added. To appear in Comm. Contemp. Mat
A Prehistory of n-Categorical Physics
This paper traces the growing role of categories and n-categories in physics,
starting with groups and their role in relativity, and leading up to more
sophisticated concepts which manifest themselves in Feynman diagrams, spin
networks, string theory, loop quantum gravity, and topological quantum field
theory. Our chronology ends around 2000, with just a taste of later
developments such as open-closed topological string theory, the
categorification of quantum groups, Khovanov homology, and Lurie's work on the
classification of topological quantum field theories.Comment: 129 pages, 8 eps figure
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