Kategoria BISAC: Mathematics >> Algebra - Abstract

The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras...

Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren spezifischen Konstruktionen herausgearbeitet.
Dieses Buch gibt eine systematische Einfuhrung in die Grundbegriffe der Kategorientheorie. Zahlreiche ausfuhrliche Erklarungstexte sowie die groe Menge an Beispielen helfen beim Einstieg in diese verhaltnismaig abstrakte Theorie. Es werden viele konkrete Anwendungen besprochen, welche die Nutzlichkeit der Kategorientheorie im mathematischen Alltag belegen. Jedes Kapitel wird mit...

This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via -universal properties-, a view on that group -from the outside-. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects.

By introducing protomodular categories and Mal'tsev categories, which form a larger class, the structural properties of the...

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.

Part of the...

This volume presents the lecture notes from the authors' three summer courses offered during the program "Automorphisms of Free Groups: Geometry, Topology, and Dynamics," held at the Centre de Recerca Matematica (CRM) in Bellaterra, Spain.

The first two chapters present the basic tools needed, from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is sufficient to present full proofs of many of the...