Angel "Java" Lopez en Blog

Teoría de Grupos, Enlaces y Recursos (1)

Publicado el 28 de Agosto, 2012, 14:02

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