by Shlomo Sternberg
Number of pages: 198
The Campbell Baker Hausdorff formula, sl(2) and its representations, classical simple algebras, Engel-Lie-Cartan-Weyl, conjugacy of Cartan subalgebras, simple finite dimensional algebras, cyclic highest weight modules, Serre’s theorem, Clifford algebras and spin representations, Kostant Dirac operator, the center of U(g).
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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 David Surowski
A set of notes for a Higher Algebra course. It covers Group Theory, Field and Galois Theory, Elementary Factorization Theory, Dedekind Domains, Module Theory, Ring Structure Theory, Tensor Products, Zorn’s Lemma and some Applications.
by Iain Gordon - University of Edinburgh
Contents: Central extensions; Virasoro algebra; Heisenberg algebra; Enveloping algebras; Hands-on loop and affine algebras; Simple Lie algebras; Kac-Moody Lie algebras; Dynkin diagrams; Forms, Weyl groups and roots; Root spaces; Affine Lie algebras.
by Douglas Lundholm, Lars Svensson - arXiv
These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.