Introduction to Lie Groups

(18.755)

This course is to serve as an introduction to the theory of Lie groups (this probably was not realy informative...). The fundamental aim of the class is to get some familiarity with Lie groups, Lie algebras, their relations (and how far the relations go), and linear groups. This should cover about 3/5 of the course. For the rest I am thinking of doing representation theory of complact Lie groups (and some more advanced structure theory, maybe) but all this can be changed depending on the interest of the class.

Books etc.:There are very many books for Lie groups, most of which are plenty for this course. I will be mainly following the following books

Office Hours: By email (altug at mit)...

TA:Pablo Boixeda Alvarez (pboixeda at mit)

Grading

Grading will be by weekly homework sets. I will assign homework on Fridays and will expect them to be back by the following Friday before class (you can email me the homework or hand in the paper copy right before the class). For undergraduates I may also assign a short presentation of their favorite Lie groups related topic (within reason...), but that is TBD.

Homework Sets

(18.755)

This course is to serve as an introduction to the theory of Lie groups (this probably was not realy informative...). The fundamental aim of the class is to get some familiarity with Lie groups, Lie algebras, their relations (and how far the relations go), and linear groups. This should cover about 3/5 of the course. For the rest I am thinking of doing representation theory of complact Lie groups (and some more advanced structure theory, maybe) but all this can be changed depending on the interest of the class.

Books etc.:There are very many books for Lie groups, most of which are plenty for this course. I will be mainly following the following books

- Lie Groups, Bump D. (Watch out for typos!)

- Foundations of Differentiable Manifolds and Lie Groups, Warner F. W.

Office Hours: By email (altug at mit)...

TA:Pablo Boixeda Alvarez (pboixeda at mit)

Grading

Grading will be by weekly homework sets. I will assign homework on Fridays and will expect them to be back by the following Friday before class (you can email me the homework or hand in the paper copy right before the class). For undergraduates I may also assign a short presentation of their favorite Lie groups related topic (within reason...), but that is TBD.

Homework Sets

- HW1 (Solutions)
- HW2 (Solutions)
- HW3 (Solutions)
- HW4 (Solutions)
- HW5 (Solutions)
- HW6 (Solutions)
- HW7 (Solutions)
- HW8 (Solutions)