Infinite dimensional Representations of 2 groups is popular PDF and ePub book, written by Anonim in 2012, it is a fantastic choice for those who relish reading online the Categories genre. Let's immerse ourselves in this engaging Categories book by exploring the summary and details provided below. Remember, Infinite dimensional Representations of 2 groups can be Read Online from any device for your convenience.
Infinite dimensional Representations of 2 groups Book PDF Summary
A `2-group' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations on `2-vector spaces', which are categories analogous to vector spaces. Unfortunately, Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional 2-vector spaces called `measurable categories' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie 2-groups. Here we continue this work. We begin with a detailed study of measurable categories. Then we give a geometrical description of the measurable representations, intertwiners and 2-intertwiners for any skeletal measurable 2-group. We study tensor products and direct sums for representations, and various concepts of subrepresentation. We describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory. We study irreducible and indecomposable representations and intertwiners. We also study `irretractable' representations--another feature not seen in ordinary group representation theory. Finally, we argue that measurable categories equipped with some extra structure deserve to be considered `separable 2-Hilbert spaces', and compare this idea to a tentative definition of 2-Hilbert spaces as representation categories of commutative von Neumann algebras.
Detail Book of Infinite dimensional Representations of 2 groups PDF
- Author : Anonim
- Release : 28 June 2024
- Publisher : Unknown
- ISBN : 0821891162
- Genre : Categories
- Total Page : 120 pages
- Language : English
- PDF File Size : 11,5 Mb
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