Infinite-dimensional Lie Algebras
by Iain Gordon
Publisher: University of Edinburgh 2009
Number of pages: 55
Contents: Central extensions; The Virasoro algebra; The Heisenberg algebra; Enveloping algebras; A little infinite-dimensional surprise; Hands-on loop and affine algebras; Simple Lie algebras; Kac-Moody Lie algebras; Classification of generalised Cartanmatrices; Dynkin diagrams; Forms, Weyl groups and roots; Root spaces; Affine Lie algebras and Kac-Moody Lie algebras; etc.
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by Leonard Evens - Northwestern University
Contents: Groups; Group actions on sets; Normal series; Ring theory; Modules; Hom and tensor; Field theory; Galois theory; Applications of Galois theory; Infinite extensions; Categories; Multilinear algebra; More ring theory; Localization; etc.
by George B. Seligman - American Mathematical Society
The purpose of the present memoir is to demonstrate the applicability, under certain restrictions on the algebra and the base field, of the techniques used in the determination of all simple Lie algebras of characteristic zero.
by Pierre Schapira - University of Luxemburg
These lecture notes are an elementary introduction to the language of categories and sheaves. From the table of contents: Linear algebra over a ring; The language of categories; Sheaves (Flabby sheaves and soft sheaves, Cohomology of sheaves).
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This introduction to the classical theory of invariants of algebraic forms is divided into three parts: linear transformations; algebraic properties of invariants and covariants; symbolic notation of Aronhold and Clebsch.