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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 |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2012.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1032. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Infinite-dimensional representations of 2-groups / |c John C. Baez [and others]. |
| 264 | 1 | |a Providence, R.I. : |b American Mathematical Society, |c ©2012. | |
| 300 | |a 1 online resource (v, 120 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v number 1032 | |
| 500 | |a "September 2012, volume 219, number 1032 (end of volume)." | ||
| 504 | |a Includes bibliographical references (pages 117-120). | ||
| 505 | 0 | |a Introduction -- Representations of 2-Groups -- Measurable Categories -- Representations on Measurable Categories -- Conclusion -- Appendix A. Tools from Measure Theory. | |
| 588 | 0 | |a Print version record. | |
| 520 | 3 | |a "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." | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Representations of groups. | |
| 650 | 0 | |a Categories (Mathematics) | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 6 | |a Catégories (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Categories (Mathematics) |2 fast | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 700 | 1 | |a Baez, John C., |d 1961- |1 https://id.oclc.org/worldcat/entity/E39PBJcGmvjFYppwRWkm6xfDv3 | |
| 776 | 0 | 8 | |i Print version: |t Infinite-dimensional representations of 2-groups |z 9780821872840 |w (DLC) 2012015625 |w (OCoLC)794640216 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1032. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114393 |z Texto completo |
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