Algebraic groups and lie groups with few factors / Alfonso Di Bartolo, Giovanni Falcone, Peter Plaumann... [et al.]

Auteur: Di Bartolo, Alfonso - AuteurCo-auteur: Plaumann, Peter - Auteur ; Falcone, Giovanni (1972-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1944Langue: anglaisÉditeur: Berlin : Springer, 2008 ISBN: 9783540785835 Note: The authors study both algebraic groups and real and complex Lie groups by imposing on their connected subgroups the analogues of familiar conditions in abstract group theory. In particular, chains of connected subgroups play a central role. An algebraic group whose connected subgroup lattice is a chain is called a chain. A class of examples are the commutative Witt groups. Also, the abstract concept of normal subgroup and generalizations find suitable concepts in the present study. In particular Hamiltonian algebraic groups are defined and investigated. A theme the authors provide is the difference between algebraic groups of characteristic zero and p. They study maximal nilpotency class, the analogue of current topics of interest in p-groups and Lie algebras. There is a long chapter on the topic of isogeneous factors. This book serves as a valuable resource to those working in the field of algebraic groups and as a good place to learn about this aspect of that field. (Zentralblatt) Sujets MSC: 20G15 Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields
22E10 Topological groups, Lie groups -- Lie groups -- General properties and structure of complex Lie groups
22E15 Topological groups, Lie groups -- Lie groups -- General properties and structure of real Lie groups
14L17 Algebraic geometry -- Algebraic groups -- Affine algebraic groups, hyperalgebra constructions
17B45 Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Lie algebras of linear algebraic groups
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The authors study both algebraic groups and real and complex Lie groups by imposing on their connected subgroups the analogues of familiar conditions in abstract group theory. In particular, chains of connected subgroups play a central role. An algebraic group whose connected subgroup lattice is a chain is called a chain. A class of examples are the commutative Witt groups. Also, the abstract concept of normal subgroup and generalizations find suitable concepts in the present study. In particular Hamiltonian algebraic groups are defined and investigated.

A theme the authors provide is the difference between algebraic groups of characteristic zero and p. They study maximal nilpotency class, the analogue of current topics of interest in p-groups and Lie algebras. There is a long chapter on the topic of isogeneous factors.

This book serves as a valuable resource to those working in the field of algebraic groups and as a good place to learn about this aspect of that field. (Zentralblatt)

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