| Type of Document |
Dissertation |
| Author |
Siehler, Jacob A.
|
| Author's Email Address |
jsiehler@math.vt.edu |
| URN |
etd-04182003-143702 |
| Title |
Near-Group Categories |
| Degree |
PhD |
| Department |
Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Quinn, Frank S. |
Committee Chair |
| Green, Edward L. |
Committee Member |
| Haskell, Peter E. |
Committee Member |
| Linnell, Peter A. |
Committee Member |
| Shimozono, Mark M. |
Committee Member |
|
| Keywords |
- monoidal categories
- braided categories
- quantum field theory
|
| Date of Defense |
2003-04-18 |
| Availability |
unrestricted |
Abstract
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object, so-called near-group categories. Data describing the fusion rule is reduced to an abelian group G and a nonnegative integer k. Conditions are given, in terms of G and k, for the existence or nonexistence of coherent associative structures for such fusion rules (ie, solutions to MacLane's pentagon equation). An explicit construction of matrix solutions to the pentagon equations is given for the cases where we establish existence, and classification of the distinct solutions is carried out partially. Many of these associative structures also support (braided) commutative and tortile structures and we indicate when the additional structures are possible. Small examples are presented in detail suitable for use in computational applications.
|
| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
|
| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
dissert.pdf |
1.28 Mb |
00:05:54 |
00:03:02 |
00:02:39 |
00:01:19 |
00:00:06 |
|
