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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 5th 2011
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   Author: zskoda
   Format: MarkdownItexArticle page (unfinished but already has a sensible story) [[Reconstruction of Groups]].

   Article page (unfinished but already has a sensible story) Reconstruction of Groups.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 5th 2011
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   Author: Urs
   Format: MarkdownItexI have added links to that page from "Tannaka duality" and "Tannaka-Krein theorem"

   I have added links to that page from “Tannaka duality” and “Tannaka-Krein theorem”

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 5th 2011
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   Author: zskoda
   Format: MarkdownItexNotice an interesting discussion at the beginning of the paper on the relation between the functional analysis picture and algebraic geometry: > Note that the Tannaka–Krein duality reflects the fact that any compact group is the set of real points of an affine pro-algebraic group (‘pro-’ stands for projective limit). This observation had lead to an extension of Tannaka–Krein duality to pro-algebraic groups ([D], [DM], [R1], [S]) and Lie algebras ([H-C], [R1]). > Continuous finite-dimensional representations of compact groups are rigid in the following sense: every subcategory of the category $f. Rep(G)$ of finite-dimensional representations of a compact group $G$, which separates elements of $G$ and is closed under the tensor product and complex conjugation, is naturally equivalent to the category $f. Rep(G)$ itself. This is a consequence of a similar rigidity property of regular representations of affine pro-algebraic groups. It follows from the results of this paper that infinite-dimensional representations of an arbitrary locally compact or Lie group do not possess the rigidity property.

   Notice an interesting discussion at the beginning of the paper on the relation between the functional analysis picture and algebraic geometry:

   Note that the Tannaka–Krein duality reflects the fact that any compact group is the set of real points of an affine pro-algebraic group (‘pro-’ stands for projective limit). This observation had lead to an extension of Tannaka–Krein duality to pro-algebraic groups ([D], [DM], [R1], [S]) and Lie algebras ([H-C], [R1]).

   Continuous finite-dimensional representations of compact groups are rigid in the following sense: every subcategory of the category $f. Rep(G)$ of finite-dimensional representations of a compact group $G$, which separates elements of $G$ and is closed under the tensor product and complex conjugation, is naturally equivalent to the category $f. Rep(G)$ itself. This is a consequence of a similar rigidity property of regular representations of affine pro-algebraic groups. It follows from the results of this paper that infinite-dimensional representations of an arbitrary locally compact or Lie group do not possess the rigidity property.