Stacky Lie Groups

Stacky Lie Groups (2008)

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by Christian Blohmann

BibTeX

@MISC{Blohmann08stackylie,
    author = {Christian Blohmann},
    title = { Stacky Lie Groups},
    year = {2008}
}

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Abstract

Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles is a categorical property which is sufficient and necessary for the existence of products. Stacky Lie groups are defined as group objects in this weak 2-category. Introducing a graphic notation, it is shown that for every stacky Lie monoid there is a natural morphism, called the preinverse, which is a Morita equivalence if and only if the monoid is a stacky Lie group. As an example, we describe explicitly the stacky Lie group structure of the irrational Kronecker foliation of the torus.

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