#

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**

**Grading:**

Problem Sets 50 %

Take Home Final Exam 50 %

## Reading

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