Tannaka-Krein duality for compact groupoids II, duality
نویسندگان
چکیده
منابع مشابه
Tannaka-krein Duality for Compact Groupoids Iii, Duality Theory
This is the last in a series of papers in which we generalized the Tannaka-Krein duality to compact groupoids. In [A1] we studied the representation theory of compact groupoids. In particular, we showed that irreducible representations have finite dimensional fibres. We also proved the Schur’s lemma, Gelfand-Raikov theorem and Peter-Weyl theorem for compact groupoids. In [A2] we studied the Fou...
متن کاملTannaka-krein Duality for Compact Groupoids Ii, Fourier Transform
Abstract. In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study the Fourier and Fourier-Plancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of squa...
متن کاملTannaka-krein Duality for Compact Groupoids I, Representation Theory
In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous representations of compact groupoids. We show that irreducible representationshave finite dimensional fibres. We prove the Schur’s lemma, Gelfand-Raikov theore...
متن کاملTannaka-krein Duality for Hopf Algebroids
We develop the Tannaka-Krein duality for monoidal functors with target in the categories of bimodules over a ring. The Coend of such a functor turns out to be a Hopf algebroid over this ring. Using a result of [4] we characterize a small abelian, locally finite rigid monoidal category as the category of rigid comodules over a transitive Hopf algebroid.
متن کاملTannaka Duality Revisited
1.1. Background. The goal of this paper is to investigate algebraic stacks through their associated categories of quasi-coherent sheaves (or, better, complexes). To put this investigation in context, note that an affine scheme is completely determined by its ring of functions. Using merely the ring of functions, though, it is difficult to move beyond affine schemes. However, if one is willing t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2010
ISSN: 1846-3886
DOI: 10.7153/oam-04-32