# SYLLABUS / SCHEDULE

## Course Overview

Lecture 1, 2: | Introduction, basic definitions |

Lecture 3-5: | Engel and Lie theorems |

Lecture 6-9: | Cartan subalgebras and Cartan's criterion |

Lecture 10: | Conjugacy of Cartan subalgebras |

Lecture 11-14: | Structure of semi-simple Lie algebras |

Lecture 15-20: | Classification of simple Lie algebras |

Lecture 21: | Compact form and Weyl group |

Lecture 22: | Universal enveloping algebra, PBW theorem, Casimir element and cohomology of Lie algebras |

Lecture 23: | Weyl, Levi and Maltsev theorems |

Lecture 24: | Verma modules |

Lecture 25, 26: | Finite-dimesional representations of semisimple Lie algebras. Weyl character and dimension formulae |

## Recommended Books

- J.P. Serre, "Complex Semi Simple Lie Algebras"
- J.E. Humphreys, "Introduction to Lie Algebras and Representation Theory"
- A.L. Onishchik, E.B. Vinberg, "Lie Groups and Algebraic Groups"

## Course Requirements

- Typing tow lectures (using TeX is preferred, MS Word is ok; contact typers of previous lectures of templates). Lecture notes should be handed in within two weeks of the date of the lecture.
- Doing exercises given in the course of lecture; collected and graded weekly. The exercises from the previous two lectures are due every Tuesday (if holiday, then the next Tuesday).