Quantum groupoids and dynamical categories

Details Quantum groupoids and dynamical categories Quantum groupoids and dynamical categories

2003-11-18

arxiv.org/abs/math/0311316v2

Mathematics

Quantum Algebra

Ex.2.6.5 and misprint in sign of \varpi on p.36 corrected. Other mostly cosmetic improvements

Scientific paper

In this paper we realize the dynamical categories introduced in our previous paper as categories of modules over bialgebroids; we study the bialgebroids arising in this way. We define quasitriangular structure on bialgebroids and present examples of quasitriangular bialgebroids related to the dynamical categories. We show that dynamical twists over an arbitrary base give rise to bialgebroid twists. We prove that the classical dynamical r-matrices over an arbitrary base manifold are in one-to-one correspondence with a special class of coboundary Lie bialgebroids.

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