MATH 453: Topology 2

MATH 453	CRN 593, 15 Points (2009 2/3)
Coordinator:	AProf Peter Donelan
Recommended:	MATH 311
Recommended Reading:	K Erdmann and M J Wildon: Introduction to Lie Algebras, B Hall: Lie Groups, Lie Algebras, and Representations
Textbook:	W Fulton and J Harris: Representation Theory, a First Course
Description:	Lie (pronounced "lee") groups are sets of transformations preserving some geometric structure, such as the set of orthogonal transformations of a Euclidean space which preserve the Euclidean inner product. They have two compatible structures: they satisfy the axioms of a group and they also depend continuously on parameters so form a differentiable manifold. Associated to any Lie group is its Lie algebra of infinitesimal transformations. Lie algebras can be studied in their own right. One can understand a great deal about a Lie group by studying its representations - actions of the group on vector spaces. Lie theory is deeply connected with the development of mathematical physics, through special relativity and quantum theory. The classification of certain types of Lie groups and algebras is one of the masterpieces of 20th century mathematics. In this course the concepts of Lie group and algebra will be introduced together with the key examples, the classical groups. The ideas underlying their classification will be developed. ONLY ONE OF MATH 453 / MATH 462 WILL BE OFFERED IN 2009
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