Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
Lie Algebras Algebraic Groups and Lie Groups
This book is an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. This book contains below topics, Lie Algebras, Algebraic Groups, III Lie groups, A Arithmetic Subgroups.
Author(s): J.S. Milne
186 Pages
Notes on G2 The Lie algebra and the Lie group
This note contains below topics, A summary of the KillingCartan classification via roots, A first linear model of split G2, Understanding G2 better, Generic 3 forms in F7, G2 and the spheres in dimension 6, G2 and spinors.
Author(s): Cristina Draper
50 Pages
The Lie group Lie algebra correspondence in tangent categories
This note contains below topics, Lie Groups in tangent categories, The Lie functor of a group object, The representability of the Lie functor, The differential Lie algebra of a Lie group, The Lie groupLie algebra correspondence.
Author(s): Marcello Lanfranchi
55 Pages
Lecture notes on Cherednik algebras
This note contains below topics, Classical and quantum OlshanetskyPerelomov systems for finite Coxeter groups, The rational Cherednik algebra, The MacdonaldMehta integral, Parabolic induction and restriction functors for rational Cherednik algebras, The KnizhnikZamolodchikov functor, Rational Cherednik algebras and Hecke algebras for varieties with group actions, Symplectic reflection algebras, CalogeroMoser spaces, Quantization of ClaogeroMoser spaces.
Author(s): Pavel Etingof, Xiaoguang Ma
92 Pages
Introduction to Lie Groups by Alistair Savage
This note focus on the socalled matrix Lie groups since this allows us to cover the most common examples of Lie groups in the most direct manner and with the minimum amount of background knowledge. Topics covered includes, Matrix Lie groups, Topology of Lie groups, Maximal tori and centres, Lie algebras and the exponential map, Covering groups.
Author(s): Alistair Savage
111 Pages
Lie Algebras and Representation Theory
The aim of this note is to develop the basic general theory of Lie algebras to give a first insight into the basics of the structure theory and representation theory of semi simple Lie algebras. Topics covered includes, Group actions and group representations, General theory of Lie algebras, Structure theory of complex semisimple Lie algebras, Cartan subalgebras, Representation theory of complex semisimple Lie algebras, Tools for dealing with finite dimensional representations.
Author(s): Andreas Cap
102 Pages
This note covers the following topics, Universal envelopping algebras, Levis theorem, Serres theorem, KacMoody Lie algebra, The Kostants form of the envelopping algebra and A beginning of a proof of the Chevalleys theorem.
Author(s): David Kazhdan
NA Pages
Matrix Lie Groups And Control Theory
This note covers the following topics, Matrix and Lie Groups, Dynamics and Control on Matrix Groups, Optimality and Riccati Equations, Geometric Control.
Author(s): Jimmie Lawson
60 Pages
