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Infinite-dimensional representations of 2-groups /
"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-gr...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2012.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1032. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "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." |
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| Notas: | "September 2012, volume 219, number 1032 (end of volume)." |
| Descripción Física: | 1 online resource (v, 120 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 117-120). |
| ISBN: | 9780821891162 0821891162 |
| ISSN: | 0065-9266 ; |