Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-49-15-K-6

Introduction to Tensor Categories (2V, 3.0 LP)

Course Type

SWS	Type	Course Form	CP (Effort)	Presence-Time / Self-Study
2	V	Lecture	3.0 CP	28 h	62 h
(2V)			3.0 CP	28 h	62 h

Basedata

SWS	2V
CP, Effort	3.0 CP = 90 h
Position of the semester	1 Sem. irreg.
Level	[6] Master (General)
Language	[EN] English
Lecturers	Thiel, Ulrich, Prof. Dr. (PROF \| DEPT: MAT) + further Lecturers of the department Mathematics
Area of study	[MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State	[NORM] Active

Contents

categories, functors, additive and Abelian categories,
monoidal categories and functors,
Grothendieck ring, categorisation, example of categorisation of group rings.

In addition, a selection of the following topics:

Hopf algebras and quantum groups,
graphic calculus for morphisms,
braided tensor categories, band categories and knot invariants,
modular tensor categories and topological quantum field theories.

Literature

P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik: Tensor Categories,
B. Bakalov, A. Kirillov: Lectures on Tensor Categories and Modular Functor,
V. Turaev: Quantum Invariants of Knots and 3-Manifolds.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Modules:

[MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)

Courses

[MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)

Requirements for attendance (formal)

None

References to Course [MAT-49-15-K-6]

Module	Name	Context
[MAT-49-15-M-6]	Introduction to Tensor Categories	P: Obligatory	2V, 3.0 LP
Course-Pool	Name
[MAT-40-2V-KPOOL-4]	Elective Courses Algebra, Geometry and Computeralgebra (2V, B.Sc.)