## Pavel Etingof

Lie Groups and Lie Algebras

### About the Book

The book is based on a year-long graduate sequence on Lie groups and Lie algebras taught by the author at MIT. It is split into 51 sections, roughly corresponding to 1.5-hour lectures. The first half (Sections 1-26) gives an introduction into the basic theory of Lie groups and Lie algebras and then works out the structure, classification and representation theory of complex semisimple Lie algebras, ending with the Weyl character formula. The second half (Sections 27-51) treats more advanced topics, such as Schur-Weyl duality, representations of classical groups, Peter-Weyl theorem for compact topological groups, a representation-theoretic treatment of the hydrogen atom, classification of real semisimple Lie algebras, structure of real semisimple Lie groups, Cartan and Iwasawa decomposition, cohomology of Lie groups and homogeneous spaces, flag varieties, and others.

### About the Author

**Pavel Etingof** is a Professor of Mathematics at MIT (since 2005) and the Chief Research Advisor of the MIT PRIMES Program (Program for Research in Mathematics, Engineering and Science for High School Students) since 2010.

Etingof received an M.S. in Applied Mathematics from the Moscow Oil & Gas Institute in 1989, and a Ph.D. in Mathematics from Yale University in 1994. Igor Frenkel was his thesis advisor. He went to Harvard as a Benjamin Peirce Assistant Professor in 1994, and joined the MIT mathematics faculty as Assistant Professor in 1998, and Professor in 2005. Etingof’s research interests are primarily in studies which intersect representation theory and mathematical physics, such as quantum groups. He serves as chief editor of the Journal of the AMS and of Selecta Math. He has co-authored 8 texts. He served as Chair of the Graduate Student Committee from 2002-05. In 1999 Etingof received a Clay Mathematics Institute Prize fellowship. In 2012 he was selected to be the Robert E. Collins Distinguished Scholar in the Mathematics Department. He was named a Fellow of the AMS in the 2013 Inaugural Class. He was selected by the Institute for the Frank E. Perkins Award for excellence in graduate advising in 2015, and again in 2018. In 2016 he was elected Fellow of the American Academy of Arts and Sciences.

### Managing Editors

- Colin Adams
- Eric Friedlander
- Sergei Tabachnikov

### Editorial Board

- George Andrews
- Colin Adams
- Eric Friedlander
- Robert Ghrist
- Joel Hass
- Robion Kirby
- Alex Kontorovich
- Sergei Tabachnikov

### AMR Research Monographs

Volume 4

**ISBN: 978-1-959384-04-5**

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