Numerical generation of semisimple tortile categories coming from quantum groups

In this work we set up a general framework for exact computations of the associativity, commutativity and duality morphisms in a quite general class of tortile categories. The source of the categories we study is the work of Gelfand and Kazhdan, Examples of tensor categories, Invent.Mlath. 109 (l992), 595-617. They proved that, associated to the quantized enveloping algebra of any simple Lie group at a primitive prime root of unity, there is a semisimple monoidal braided category with finite number of simple objects. The prime p needs to be greater than the Coxeter number of the corresponding Lie algebra. We show that each of the Gelfand-Kazhdan categories has at least two subcategories which are tortile, and offer algorithms for computing the associativity, commutativity and duality morphisms in any of those categories. A careful choice of the bases of the simple objects and of the product of two such objects rnake the exact computations possible. The algorithms have been implemented in Mathemetica and tested for the categories A₂,p=5, A₃,p=7, A₄.p=7, C₂,p=7, and G₂,p=11. This work was supported by the Center for Mathematical Computations through NSF grant DMS-9207973.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1996

Author dc:creator

• Bobtcheva, Ivelina

Chair dc:contributor.committeechair

• Quinn, Frank S.

Committee members dc:contributor.committeemember

• Green, Edward L.
• Haskell, Peter E.
• Letzter, Gail
• Linnell, Peter A.

• quantum groups
• representations
• 6j-symbols
• tortile category

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-06062008-151240

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/37995