Equivalence between the Morita categories of etale Lie groupoids and of locally grouplike Hopf algebroids

Details Equivalence between the Morita categories of etale Lie groupoids and of locally grouplike Hopf algebroids Equivalence between the Morita categories of etale Lie groupoids and of locally grouplike Hopf algebroids

2007-03-13

arxiv.org/abs/math/0703374v1

Indag. Math. 19 (2008) 73-96

Mathematics

Quantum Algebra

19 pages

Scientific paper

Any etale Lie groupoid G is completely determined by its associated convolution algebra C_c(G) equipped with the natural Hopf algebroid structure. We extend this result to the generalized morphisms between etale Lie groupoids: we show that any principal H-bundle P over G is uniquely determined by the associated C_c(G)-C_c(H)-bimodule C_c(P) equipped with the natural coalgebra structure. Furthermore, we prove that the functor C_c gives an equivalence between the Morita category of etale Lie groupoids and the Morita category of locally grouplike Hopf algebroids.

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