Representations of Lie Algebras

Anthony Henderson is an Associate Professor in the School of Mathematics and Statistics at the University of Sydney, where he has worked since graduating in 2001 from the Massachusetts Institute of Technology. He won the 2011 Christopher Heyde Medal of the Australian Academy of Science for his research in geometric and combinatorial aspects of representation theory and currently holds an Australian Research Council Future Fellowship. He has taught a wide range of undergraduate courses and in 2009 was awarded a Faculty of Science Citation for Excellence in Teaching.

• 1. Motivation: representations of Lie groups; 2. Definition of a Lie algebra; 3. Basic structure of a Lie algebra; 4. Modules over a Lie algebra; 5. The theory of sl2-modules; 6. General theory of modules; 7. Integral gln-modules; 8. Guide to further reading; Appendix: solutions to the exercises; References; Index.

'This short book develops the standard tools (special bases, duality, tensor decompositions, Killing forms, Casimir operators …) and aims for a single result: the classification of integral modules over gln. Requiring only basic linear algebra, this book can serve as an interesting alternative platform (to basic group theory) for introducing abstract algebra … Recommended.' D. V. Feldman, Choice