240032 Proseminar - Lie Algebras (PS) (WiSe 2022/2023)

Contents, comment

A Lie algebra is a vector space together with a bilinear operation called the Lie bracket, denoted [-,-]. An example is given by the Lie algebra of n by n matrices over the complex numbers with the Lie bracket defined by [x,y] = xy-yx. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds, for example the general linear group, or the orthogonal group. Lie algebras appear as 'infinitessimal symmetries' of spaces, which is especially important in physics. The aim in this proseminar is to give an easy introduction to Lie algebras, hopefully getting as far as the classification of complex simple Lie algebras in terms of Dynkin diagrams

Requirements for participation, required level

Students need a very good understanding of linear algebra, from the courses Linear Algebra I and II.

Bibliography

  • K. Erdmann and M. J. Wildon, Introduction to Lie algebras, Springer 2006. University Library: Ebook, QA080+QA260 E66 and QA260 E66.
  • J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer 1972-2001. University Library: QA260 H927.
  • R. W. Carter, Lie algebras of finite and affine type, CUP 2005. University Library: QA260 C324.

External comments page

https://www.math.uni-bielefeld.de/~wcrawley/2223Liealgebras/

Teaching staff

Dates ( Calendar view )

Frequency Weekday Time Format / Place Period  
one-time Fr 10:15-11:45 V4-116 15.07.2022 Organisational meeting
weekly Fr 10-12 C01-148 10.10.2022-03.02.2023
not on: 12/30/22 / 1/6/23

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Subject assignments

Module Course Requirements  
24-B-GEO_ver1 Geometrie (Gym/Ge) Proseminar Study requirement
Ungraded examination
Student information
24-B-PX Praxismodul Proseminar Study requirement
Ungraded examination
Student information

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Registered number: 6
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Limited number of participants: 15
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WS2022_240032@ekvv.uni-bielefeld.de
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Last update basic details/teaching staff:
Monday, June 13, 2022 
Last update times:
Friday, July 29, 2022 
Last update rooms:
Friday, July 29, 2022 
Type(s) / SWS (hours per week per semester)
proseminar (PS) / 2
Language
This lecture is taught in english
Department
Faculty of Mathematics
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359631122