Spring 2013 Course Syllabus - Mathematics 9110.001
Course: Mathematics 9110.001.
Course Title: Topics in Algebra: Representation Theory II.
Time: TR 0930-1050.
Place: Wachman Hall CC447.
Instructor: Lorenz, Martin W.
Instructor Office: Wachman Hall CC528.
Instructor Email: martin.lorenz@temple.edu
Instructor Phone: 215-204-5013.
Office Hours: TR 11:00-12:00 or by appointment.
Prerequisites: Some familiarity with the material covered in Math 9100 is assumed, specifically the basic facts concerning representations of algebras.
Textbook: The course does not follow any particular textbook. As background references for the this semester, I recommend the following books: -- James Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics Vol. 9, Springer-Verlag, New York, 1972. -- William Fulton and Joe Harris, Representation Theory, A First Course, Graduate Texts in Mathematics Vol. 129, Springer-Verlag, New York, 1991.
Course Goals: This two-semester course gives an introduction to the principal methods and results of algebraic representation theory. The second semester will mainly be devoted to representations of finite-dimensional Lie algebras, with particular emphasis on the case of semisimple Lie algebras.
Topics Covered: Definition of Lie algebras and examples; enveloping algebras and the Poincare-Birkhoff-Witt Theorem; types of Lie algebras: nilpotent, solvable, and semisimple; semisimple Lie algebras: definition and basic properties, Killing form, root space decomposition; classification of simple Lie algebras: root systems, Dynkin diagrams; highest weight modules; representation ring and WeylÂ’s character formula.
Course Grading: The course grade will be based on regular homework assignments.
Exam Dates: N/A.
Attendance Policy: Attendance will not be monitored, but you are strongly encouraged to attend class regularly and to take complete class notes.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:
- The first day of classes is Tuesday, January 22.
- The last day to drop/add (tuition refund available) is Monday, February 4.
- Spring recess is the week of Sunday, March 10 - Sunday, March 17.
- The last day to withdraw (no refund) is Tuesday, March 26.
- The last day of classes is Monday, May 6.
During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.