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## Schedule

Date | Speaker | Details | ||
---|---|---|---|---|

Sep. 29, 2019. 19:15 | Preliminary meeting. Selection of a seminar topic, administrative details, etc. | |||

Oct. 10, 2019. 20:30 | Devkota, Prabhat |
References: You can find notes here. | ||

Oct. 18, 2019. 19:30 |
References: See Sections 4.1 to 4.4 in Alexander Kirillov's notes. For a review of common linear-algebraic constructions refer to Appendix B in Fulton and Harris' "Representation Theory: A First Course" | Oct. 25, 2019. | No meeting. | |

Nov. 1, 2019. |
References: See Appendix A of Lando's Graphs on Surfaces and their Applications for a quick overview (also here). Chapters 1-2 of Serre's Linear Representations of Finite Groups are also useful. | |||

Nov. 8, 2019 | First look at the classification of connected Abelian Lie groups and connected complex Abelian Lie groups. References: The notes can be found here. | |||

Nov 15, 2019 | Aryal, Deepak | Killing form, solvable, nilpotent and semi-simple lie algebras, existence of maximal solvable and nilpotent radical, equivalent definitions of semisimple lie algebras (in terms of killing form and direct sum of simple lie algebra). References: Page 88-90 and 95-98 of the book "Lie Groups: An approach through invariants and representations" by Claudio Procesi. | ||

Nov 22, 2019 |
- Cartan subalgebras, root sets, dual of Cartan subalgebras, root systems, Dynkin diagrams.
References: Fulton and Harris, Part IV section 21.1, Frederic Schuller - Classification of Lie algebras and Dynkin diagrams | |||

Nov 29, 2019 | Oprea, Maria Antonia | Representations of sl(2, C) | ||

Dec 28, 2019 | Devkota, Prabhat | The Levi-Malcev theorem | ||

Jan. 11, 2020 | Pal, Abhik |
References: Humphreys "Introduction to Lie Algebra and Representation Theory" Part 3 sections 9-11. | ||

19:00. Jan. 19, 2020 |
References: For background on algebraic groups: Malle-Testermann's Linear Algebraic Groups and Finite Groups of Lie Type (Chapters 1 and 6), or Milne's Algebraic Groups, available here. For real forms I used Onishchik-Vinberg's Lie Groups and Lie Algebras III. |

## General Information

### Meeting time, location

19:30. Room 120 (Seminar Room), Research

### Participants

Pal, AbhikAryal, Deepak Irungu, Martin Waiharo Falkenburg, Pia Cosma Devkota, Prabhat Blloshmi, Denida Mele, Crystal Oprea, Maria Antonia