Module Handbook

  • 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
+ 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:

Courses

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.)