Math 845 Notes on Lie Groups
نویسنده
چکیده
1 Quaternions and the three-dimensional sphere 3 1.1 Hamiltion’s quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Lie group S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 The normalizer of Q8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 The exponential map for S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
منابع مشابه
Math 229a Fall 2014 Class Notes
Please let me know if you find any mistakes! Friday, October 3, 2014. Grading will be based on an exam on Friday, December 12. Groups of general interest often have some additional natural structure: Topological groups, Lie groups. From Lie groups, we get Lie algebras via a standard procedure in differential topology. There’s also an association in the reverse direction, from Lie algebras to Li...
متن کاملNotes on the Riemannian geometry of Lie groups
Lie groups occupy a central position in modern differential geometry and physics, as they are very useful for describing the continuous symmetries of a space. This paper is an expository article meant to introduce the theory of Lie groups, as well as survey some results related to the Riemannian geometry of groups admitting invariant metrics. In particular, a non-standard proof of the classific...
متن کاملIrreducible Modular Representations of Finite and Algebraic Groups
In these notes we outline some aspects of the modular representation theories of finite groups of Lie type in defining and cross-characteristics, with particular interest paid to how these theories relate to the modular representation theory of algebraic groups and the (characteristic 0) representation theory of Lie algebras and quantum groups. We begin by summarizing some classical results on ...
متن کاملMath 263: Infinite-Dimensional Lie Algebras
Our text will be Kac, Infinite-Dimensional Lie Algebras (third edition) though I will also rely on Kac and Raina, Bombay Lectures on Highest Weight Representations of InfiniteDimensional Lie Algebras . I will assume you have access to the first text but not the second. Unfortunately Kac’ book is long and dense. These notes are an attempt to make a speedy entry. Most relevant for the first part ...
متن کاملCorrection to Abstract Class Formations by K. Grant and G. Whaples
1. A. Borel and Harish-Chandra, Arithmetic subgroups of algebraic groups, Bull. Amer. Math. Soc. 67 (1961), 579-583. 2. , Arithmetic subgroups of algebraic groups, Ann. of Math. (2) 75 (1962), 485-535. 3. Harish-Chandra, On the characters of a semisimple Lie group, Bull. Amer. Math. Soc. 61 (1955), 389-396. 4. , Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87-12...
متن کامل