Lie Algebra
(Math 7360)
Section |
Place |
Time |
||||
Math 7360-140 |
Parker 248 |
MWF |
14:00-14:50 |
Fri |
May 6 |
16:00-18:30 |
1.
Complex semisimple Lie algebras,
Jean-Pierre Serre, Springer, Berlin Heidelberg, 1987.
2.
Lie Algebras, Nathan Jacobson, Dover, New York, 1979.
3.
Lie groups beyond an introduction, Chapters I & II,
Anthony W. Knapp, 2002.
4.
Modular Lie Algebras and Their Representations, Helmut Strade and Rolf Farnsteiner, Pure
and Applied Mathematics, Marcel Dekker, New York, 1988.
· Lie
algebras, subalgebras, linear Lie algebras and linear
groups, adjoint representations, abelian Lie algebras.
· Ideals,
centers, derived algebras, simple algebras, quotient algebras, homomorphisms, representations.
· Solvable Lie
algebras, radical, semisimple Lie algebras, nilpotent
Lie algebras, Engel's Theorem.
· Lie's
Theorem, Jordan-Chevalley decomposition, Cartan's Criterion for solvable Lie algebras.
· Killing
forms, radicals, simple ideals, inner derivations, abstract Jordan
decompositions.
· Lie algebra
modules, module homomorphisms, irreducible modules,
completely reducible modules, Schur's Lemma, Casimir
element, Weyl's Theorem, preservation of Jordan decomposition.
· Representations
of sl(2,F).
· Toral subalgebras, root space decomposition (Cartan
decomposition), properties of maximal toral subalgebras.
· Reflections,
root system, roots, dual root system, base, Weyl chambers, Weyl group.
· Cartan matrix, Cartan integers, Coxeter graphs, Dynkin diagrams, classification of simple Lie algebras, automorphisms of root systems.
· Weights,
root lattices, half sum of positive roots, highest weight, saturated sets of
weights.
Grade |
A |
B |
C |
D |
F |
Score |
90-100 |
80-89 |
70-79 |
60-69 |
0-59 |
§ Chapter 1 Chapter 2 Chapter 3