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Ya escribí varios posts sobre teoría de grupos (ver por ejemplo Simetrías del Cuadrado, Teoría de Galois, Motivaciones para Teoría de Grupos). Venga hoy una primera colección de enlaces sobre este tema que me interesa desde hace más de treinta años.
http://en.wikipedia.org/wiki/Group_theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced tremendous advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, can be modelled by symmetry groups. Thus group theory and the closely related representation theory have many applications in physics and chemistry.
One of the most important mathematical achievements of the 20th century[1] was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 1980, that culminated in a complete classification of finite simple groups.
Algebra Representations http://unapologetic.wordpress.com/2008/10/24/algebra-representations/
Representation Theory II http://hilbertthm90.wordpress.com/2009/07/06/representation-theory-ii/
Group Representations http://unapologetic.wordpress.com/2008/10/23/group-representations/
Lie groups, Lie algebras, and representations http://unapologetic.wordpress.com/2007/03/20/lie-groups-lie-algebras-and-representations/
Lie groups in nature http://drmathochist.wordpress.com/2010/01/11/lie-groups-in-nature/
Reading seminar 6: "Stable group theory and approximate subgroups", by Ehud Hrushovski http://terrytao.wordpress.com/2009/12/04/reading-seminar-6-stable-group-theory-and-approximate-subgroups-by-ehud-hrushovski/
GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra http://www.gap-system.org/ GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects.
Open question: noncommutative Freiman theorem http://terrytao.wordpress.com/2007/03/02/open-question-noncommutative-freiman-theorem/
An elementary non-commutative Freiman theorem http://terrytao.wordpress.com/2009/11/10/an-elementary-non-commutative-freiman-theorem/
Why do Groups and Abelian Groups feel so different? http://mathoverflow.net/questions/2551/why-do-groups-and-abelian-groups-feel-so-different
Group Theory http://arxiv.org/list/math.GR/recent
The development of group theory http://www-history.mcs.st-and.ac.uk/HistTopics/Development_group_theory.html
Nilpotent group http://en.wikipedia.org/wiki/Nilpotent_group
History of group theory http://en.wikipedia.org/wiki/History_of_group_theory
Carter subgroup http://en.wikipedia.org/wiki/Carter_subgroup
Centralizer and normalizer http://en.wikipedia.org/wiki/Self-normalizing
Como armar el cubo de Rubik en segundos http://videosdetv.blogspot.com.ar/2007/02/como-armar-el-cubo-de-rubik-en-segundos.html
GROUP PROPERTIES AND GROUP ISOMORPHISM http://math.ucsd.edu/~jwavrik/honors/manalo.pdf
First Group Isomorphism Theorem http://mathworld.wolfram.com/FirstGroupIsomorphismTheorem.html
How Mathematicians Study Symmetry http://web.maths.unsw.edu.au/~danielch/algebra07a/qinnotes.pdf
Group Theory - J.S. Milne http://www.jmilne.org/math/CourseNotes/gt.html
Groups Theory Books http://www.freebookcentre.net/Mathematics/Groups-Theory-Books.html
How to write down the representations of GL_n http://sbseminar.wordpress.com/2008/07/08/how-to-write-down-the-representations-of-gl_n/
Finite Group Theory http://www.wolfram.com/products/mathematica/newin7/content/FiniteGroupTheory/
Group Theory http://www.dmoz.org/Science/Math/Algebra/Group_Theory/
ATLAS of Finite Group Representations http://brauer.maths.qmul.ac.uk/Atlas/
ABSTRACT ALGEBRA ON LINE http://www.math.niu.edu/~beachy/aaol/
Group Theory and Generalizations http://www.math.niu.edu/~rusin/known-math/index/20-XX.html
Mis Enlaces http://delicious.com/ajlopez/grouptheory
Nos leemos!
Angel "Java" Lopez http://www.ajlopez.com http://twitter.com/ajlopez
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