MAT 552 — Spring 2022 Problem Sets MAT 552 — Spring 2022 Syllabus

MAT 552 Course Webpage
Introduction to Lie groups and Lie algebras
M W 2:40PM — 4PM, Physics P 127

Spring 2022

  • Problem sets
  • Syllabus

  • Course Announcements
  • Course Description
  • Prerequisites
  • Text
  • Lectures
  • Office Hours
  • Disability Support Services
  • Academic Integrity
  • Critical Incident Management


  • Course Announcements Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture and/or in recitation).

    Course Description Description in the graduate bulletin. "An introduction to Lie groups and Lie algebras, as used in mathematics and physics. Basic facts about Lie groups and Lie algebras; classical groups. Structure theory of Lie algebras. Representation theory of sl (2,C). Classification of complex semisimple Lie algebras via their root systems. Examples of exceptional Lie algebras. Other possible topics include the representation theory compact Lie groups and semisimple Lie algebras (with a focus on analytic techniques)."

    A Lie group is a differentiable manifold with a smooth group structure, and the induced structure on the tangent space of the manifold at the group identity is a Lie algebra. Lie groups arise as symmetry groups in many other mathematical subjects, which makes them central objects of study. This course studies Lie groups as important examples of differentiable manifolds, but we also explore the structure theory and classification of Lie groups and Lie algebras.

    Prerequisites Students should have passed the graduate algebra sequence or its equivalent and understand the basics of differentiable manifolds.

    Text There is no required textbook. The recommended textbook is An introduction to Lie groups and Lie algebras by Prof. Alexander Kirillov, Jr. For the theory of finite-dimensional complex linear representations of complex semisimple Lie algebras, I also recommend Representation theory, a first course. by William Fulton and Joe Harris. For the algebraic side, there are excellent books by Springer, by Humphreys, by Borel, and by Bourbaki.

    Lectures The instructor for this course is Jason Starr. All instruction will occur in lectures. The tentative schedule is in the syllabus.

    Lecture is held Mondays and Wednesdays, 2:40 PM — 4 PM in Physics P 127.

    Office Hours. Here is a link to the current office hours.

    Grading System Grades are based on class participation, on performance on assigned problem sets, and on a final 20-minute oral presentation on a topic related to the course and approved by the instructor.

    Disability Support Services

    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities and search Fire Safety and Evacuation and Disabilities.

    Academic Integrity

    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html

    Critical Incident Management

    Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Until/unless the latest COVID guidance is explicitly amended by SBU, during Fall 2021 "disruptive behavior" will include refusal to wear a mask during classes.

    Back to my home page.


    Jason Starr
    4-108 Math Tower
    Department of Mathematics
    Stony Brook University
    Stony Brook, NY 11794-3651
    Phone: 631-632-8270
    Fax: 631-632-7631
    Jason Starr