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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
This note contains below topics, Review of algebraic schemes over a field, Algebraic groups over a field geometric properties, Examples of algebraic groups, Group theory, Representations, Some basic constructions, Tannaka duality and applications, The Lie algebra of an algebraic group, Groups of multiplicative type, Algebraic groups acting on schemes, Homogeneous spaces, Tori acting on schemes, Unipotent groups, Solvable algebraic groups, Borel and Cartan subgroups, Isogenies and universal covers, Semisimple and reductive groups, Split semisimple groups and their root systems.
Author(s): J.S. Milne
139 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
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
Lie Algebras and Their Representations
This note explains the following topics, Representations of sl2, Structure and classification of simple lie algebras, Structure theory of semisimple lie algebras and root systems.
Author(s): University of Cambridge
34 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
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
