Module Handbook

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Module MAT-49-15-M-6

Introduction to Tensor Categories (M, 3.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-49-15-M-6 Introduction to Tensor Categories 3.0 CP (90 h)

Basedata

CP, Effort 3.0 CP = 90 h
Position of the semester 1 Sem. irreg.
Level [6] Master (General)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-49-15-K-6
Introduction to Tensor Categories
P 28 h 62 h - - PL1 3.0 irreg.
  • About [MAT-49-15-K-6]: Title: "Introduction to Tensor Categories"; Presence-Time: 28 h; Self-Study: 62 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84156 ("Introduction to Tensor Categories")

Evaluation of grades

The grade of the module examination is also the module grade.


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.

Competencies / intended learning achievements

Upon successful completion of this module, the students have learned the fundamentals of category theory, categorical thinking and categorisation. They understand both - the theoretical principles and proofs as well as examples and applications - and are able to understand and explain them.

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 Module / Module Number [MAT-49-15-M-6]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics Pure Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Pure Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)