Lie-Rinehart algebras, Hopf algebroids with and without an antipode.

Ana Rovi (University of Glasgow)

Wednesday 12th March, 2014 16:00-17:00 Maths 204


Through the process of horizontal categorification (or oidification),  Lie groups become Lie groupoids,  Lie algebras become Lie algebroids (Lie-Rinehart algebras)  and Hopf algebras correspond to Hopf algebroids. Since the enveloping algebra of a Lie algebra is a Hopf algebra,  it is a natural question whether the enveloping algebra  of a Lie-Rinehart algebra carries the structure of a Hopf algebroid. In this talk I will give some background on these structures,  and will give an examples of Hopf algebroids without an antipode. Some of these examples and results are joint work with Uli Kraehmer.

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