This note covers the
following topics: Free algebras, Universal enveloping algebras , p th powers,
Uniqueness of restricted structures, Existence of restricted structures ,
Schemes, Differential geometry of schemes, Generalised Witt algebra,
Filtrations, Witt algebras are generalised Witt algebra, Differentials on a
scheme, Lie algebras of Cartan type, Root systems, Chevalley theorem,
Chevalley reduction, Simplicity of Chevalley reduction, Chevalley groups,
Abstract Chevalley groups, Engel Lie algebras and Lie algebra associated
to a group .
This note covers the
following topics: Solvable and nilpotent Lie algebras, The theorems of Engel and
Lie, representation theory, Cartan’s criteria, Weyl’s theorem, Root systems,
Cartan matrices and Dynkin diagrams, The classical Lie algebras, Representation
theory.
This note focus on
the so-called 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.
In these lectures we will
start from the beginning the theory of Lie algebras and their representations.
Topics covered includes: General properties of Lie algebras, Jordan-Chevalley
decomposition, semisimple Lie algebras, Classification of complex semisimple Lie
algebras, Cartan subalgebras, classification of connected Coxeter graphs and
complex semisimple Lie algebras, Poicare-Birkhoff-Witt theorem.
This book covers the following topics: Lie Groups:Basic
Definitions, Lie algebras, Representations of Lie Groups and Lie
Algebras, Structure Theory of Lie Algebras, Complex Semisimple Lie Algebras,
Root Systems, Representations of Semisimple Lie Algebras, Root Systems and
Simple Lie Algebras.
This note covers the following
topics: Ideals and homomorphism, Nilpotent and solvable Lie algebras , Jordan
decomposition and Cartan's criterion, Semisimple Lie algebras and the Killing
form, Abstract root systems, Weyl group and Weyl chambers, Classification of
semisimple Lie algebras , Exceptional Lie algebras and automorphisms,
Isomorphism Theorem, Conjugacy theorem.
This is an open source book written by Francisco Bulnes. The purpose of this book is to present a complete course on global
analysis topics and establish some orbital applications of the integration on
topological groups and their algebras to harmonic analysis and induced
representations in representation theory.
This note covers the
following topics: Free algebras, Universal enveloping algebras , p th powers,
Uniqueness of restricted structures, Existence of restricted structures ,
Schemes, Differential geometry of schemes, Generalised Witt algebra,
Filtrations, Witt algebras are generalised Witt algebra, Differentials on a
scheme, Lie algebras of Cartan type, Root systems, Chevalley theorem,
Chevalley reduction, Simplicity of Chevalley reduction, Chevalley groups,
Abstract Chevalley groups, Engel Lie algebras and Lie algebra associated
to a group .
This note explains the
following topics: Basic definitions and examples, Theorems of Engel and Lie, The
Killing form and Cartan’s criteria, Cartan subalgebras, Semisimple Lie algebras,
Root systems, Classification and examples of semisimple Lie algebras.
This book presents a simple straightforward introduction, for the
general mathematical reader, to the theory of Lie algebras, specifically to
the structure and the (finite dimensional) representations of the semisimple
Lie algebras.
This note covers the following topics: Numerical analysts in Plato’s
temple, Theory and background, Runge–Kutta on manifolds and RK-MK, Magnus and
Fer expansions, Quadrature and graded algebras, Alternative coordinates,
Adjoint methods, Computation of exponentials, Stability and backward error
analysis, Implementation, Applications.
This note covers the following topics: Applications of the Cartan calculus, category of split orthogonal vector
spaces, Super Poison algebras and Gerstenhaber algebras, Lie groupoids and Lie
algebroids, Friedmann-Robertson-Walker metrics in general relativity, Clifford
algebras.