Abelian Groups and Representations of Finite Partially Ordered Sets 0-387-98982-X, 9780387989822

Table of contents :
Content: 1 Representations of Posets over a Field.- 1.1 Vector Spaces with Distinguished Subspaces.- 1.2 Representations of Posets and Matrix Problems.- 1.3 Finite Representation Type.- 1.4 Tame and Wild Representation Type.- 1.5 Generic Representations.- 2 Torsion-Free Abelian Groups.- 2.1 Quasi-isomorphism and Isomorphism at p.- 2.2 Near-isomorphism of Finite Rank Groups.- 2.3 Stable Range Conditions for Finite Rank Groups.- 2.4 Self-Small Groups and Endomorphism Rings.- 3 Butler Groups.- 3.1 Types and Completely Decomposable Groups.- 3.2 Characterizations of Finite Rank Groups.- 3.3 Quasi-isomorphism and ?-Representations of Posets.- 3.4 Countable Groups.- 3.5 Quasi-Generic Groups.- 4 Representations over a Discrete Valuation Ring.- 4.1 Finite and Rank-Finite Representation Type.- 4.2 Wild Modulo p Representation Type.- 4.3 Finite Rank Butler Groups and Isomorphism at p.- 5 Almost Completely Decomposable Groups.- 5.1 Characterizations and Properties.- 5.2 Isomorphism at p and Representation Type.- 5.3 Uniform Groups.- 5.4 Primary Regulating Quotient Groups.- 6 Representations over Fields and Exact Sequences.- 6.1 Projectives, Injectives, and Exact Sequences.- 6.2 Coxeter Correspondences.- 6.3 Almost Split Sequences.- 6.4 A Torsion Theory and Localizations.- 7 Finite Rank Butler Groups.- 7.1 Projectives, Injectives, and Exact Sequences.- 7.2 Endomorphism Rings.- 7.3 Bracket Groups.- 8 Applications of Representations and Butler Groups.- 8.1 Torsion-Free Modules over Discrete Valuation Rings.- 8.2 Finite Valuated Groups.- References.- List of Symbols.- Index of Terms.

Polecaj historie

Combinatorics of finite sets

680 114 3MB Read more

ERGODIC ACTIONS OF COMPACT ABELIAN GROUPS

183 35 1MB Read more

Abelian Groups: Structures and Classifications 9783110427684, 9783110432114

This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abel

178 46 61MB Read more

Abelian Groups: Structures and Classifications 9783110427684, 9783110432114

This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abel

198 20 4MB Read more

Representation Theory of Finite Groups

197 10 1MB Read more

Representation Theory of Finite Groups

201 55 5MB Read more

Abelian Groups 978-3-11-042768-4

This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abel

437 83 6MB Read more

Maximal Abelian Sets of Roots [1 ed.] 9781470442088, 9781470426798

In this work the author lets $\Phi$ be an irreducible root system, with Coxeter group $W$. He considers subsets of $\Phi

164 28 2MB Read more

Sets and ordered structures 217-219-225-2

599 136 2MB Read more

Theory of groups and symmetries : finite groups, Lie groups, and Lie algebras 9789813236868, 9813236868

"The book presents the main approaches in study of algebraic structures of symmetries in models of theoretical and

1,178 237 12MB Read more