# MAT455 Advanced Topics in Geometry: Lie algebras and Lie groups Fall 2011

## Course Information

Time: W F 11:00 a.m. - 12:20 p.m.
Classroom: McDonnel 106
Instructor: Anna Wienhard, email
Office: Fine 1007
Office Hours: Wednesday after class (or email me)

Grader: Arul Shankar email Office hours: Monday 4 pm - 5 pm, Fine 311.

Syllabus

Problem Sets 50 %
Take Home Final Exam 50 %

Differentiable and Analytic Manifolds, Chapter 1 in V. Varadarajan, Lie groups, Lie algebras and their representations, Springer 1984, 1 - 35.
Differentiable Manifolds , Chapter 2 in A. Sagle and R. Walde, Introduction to Lie groups and Lie algebras, Academic Press, New York 1973, 40 - 68.
Differentiable Manifolds , Chapter 2 in A. Sagle and R. Walde, Introduction to Lie groups and Lie algebras, Academic Press, New York 1973, 68 - 89.

## Assignments

The problem sets will be posted on Fridays. It will be due the following Friday at the beginning of class.
Problem set, due September 21: Homework
Problem set, due September 28: Homework
Problem set, due October 5: Homework, Correction: in Problem 1 (2) the map f from G to H should be assumed to be a group isomorphism and f(U) should be supposed to be open. Here is a reformulation of Problem 1 (2), which is now hopefully correct: Let f: G->H be an abstract group isomorphims. Assume that there exists U\subset G and V \subset H open subsets of the identity elements such that f|_U: U \to V is a homeomorphism. Show that then f is a isomorphism of topological groups.
Problem set, due October 14: Homework
Problem set, due October 21: Homework
Problem set, due October 28: Homework
Problem set, due November 4: FALL BREAK
Problem set, due November 11: Homework
Problem set, due November 18: Homework Correction: Problem 2 (4): maximal solvable ideal.
Problem set, due November 28: Homework
Problem set, due December 2: No problem set this week, the next set will be posted on Friday, December 2, 2011.
Problem set, due December 9: Homework
Problem set, due December 16: Homework