Lectures on Algebraic Groups
by Alexander Kleshchev
Publisher: University of Oregon 2005
Number of pages: 166
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; Characteristic 0 theory; Semisimple Lie algebras; The Chevalley construction; Borel subgroups and flag varieties; The classification of reductive algebraic groups.
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by Charles F. Miller III - University of Melbourne
Lecture notes for the subject Combinatorial Group Theory at the University of Melbourne. Contents: About groups; Free groups and presentations; Construction of new groups; Properties, embeddings and examples; Subgroup Theory; Decision Problems.
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In this text, a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, is introduced.
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This book is an account of several quite different approaches to Artin's braid groups, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.
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Symmetry plays an important role in chemistry and physics. Group captures the symmetry in a very efficient manner. We focus on abstract group theory, deal with representations of groups, and deal with some applications in chemistry and physics.