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Algebras and their Representations
(dt. Algebren und Darstellungen)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. István Heckenberger

Contents

  • Fundamentals of associative algebra theory.
  • artinian, noetherian, and semisimple moduli
  • semisimple algebras and Wedderburn's theorem.
  • Decomposition theory for moduli
  • projective moduli of right artinian algebras
  • quivers of right-artic algebras
  • Quiver representations

Qualification Goals

The students

  • understand beginnings of the theory of noncommutative algebras and their representations,
  • can transfer their skills in dealing with matrices to a more abstract context,
  • understand matrices as a special case of abstract algebraic structures,
  • have deepened mathematical working methods (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in lecture and tutorials by practicing free speech in front of an audience and in discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Algebra [Bachelor Module] or Algebra [Lehramt Module].


Applicability

Module imported from M.Sc. Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.


Recommended Reading

  • R. S. Pierce, Associative Algebras, Springer, 1982
  • I. Assem, D. Simson, A. Skowro´nski, Elements of the Representation Theory of Associative Algebras, LMS Student Texts 65, 2006



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.