The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality


The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality


The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : Friedrich Wehrung
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by Friedrich Wehrung and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Boolean rings categories.




The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality


The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by K. R. Goodearl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.


Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index



Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations


Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations
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Author : Greg Hjorth
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations written by Greg Hjorth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.


This memoir is both a contribution to the theory of Borel equivalence relations, considered up to Borel reducibility, and measure preserving group actions considered up to orbit equivalence. Here $E$ is said to be Borel reducible to $F$ if there is a Borel function $f$ with $x E y$ if and only if $f(x) F f(y)$. Moreover, $E$ is orbit equivalent to $F$ if the respective measure spaces equipped with the extra structure provided by the equivalence relations are almost everywhere isomorphic. We consider product groups acting ergodically and by measure preserving transformations on standard Borel probability spaces.In general terms, the basic parts of the monograph show that if the groups involved have a suitable notion of 'boundary' (we make this precise with the definition of near hyperbolic), then one orbit equivalence relation can only be Borel reduced to another if there is some kind of algebraic resemblance between the product groups and coupling of the action. This also has consequence for orbit equivalence. In the case that the original equivalence relations do not have non-trivial almost invariant sets, the techniques lead to relative ergodicity results. An equivalence relation $E$ is said to be relatively ergodic to $F$ if any $f$ with $xEy \Rightarrow f(x) F f(y)$ has $[f(x)]_F$ constant almost everywhere.This underlying collection of lemmas and structural theorems is employed in a number of different ways. In the later parts of the paper, we give applications of the theory to specific cases of product groups. In particular, we catalog the actions of products of the free group and obtain additional rigidity theorems and relative ergodicity results in this context. There is a rather long series of appendices, whose primary goal is to give the reader a comprehensive account of the basic techniques. But included here are also some new results. For instance, we show that the Furstenberg-Zimmer lemma on cocycles from amenable groups fails with respect to Baire category, and use this to answer a question of Weiss. We also present a different proof that $F_2$ has the Haagerup approximation property.



Semisolvability Of Semisimple Hopf Algebras Of Low Dimension


Semisolvability Of Semisimple Hopf Algebras Of Low Dimension
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Author : Sonia Natale
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Semisolvability Of Semisimple Hopf Algebras Of Low Dimension written by Sonia Natale and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.


The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.



A Random Tiling Model For Two Dimensional Electrostatics


A Random Tiling Model For Two Dimensional Electrostatics
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Author : Mihai Ciucu
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

A Random Tiling Model For Two Dimensional Electrostatics written by Mihai Ciucu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Electrostatics categories.


Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.



Lattice Theory Special Topics And Applications


Lattice Theory Special Topics And Applications
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Author : George Grätzer
language : en
Publisher: Springer
Release Date : 2014-08-27

Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.


George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.



Homological And Homotopical Aspects Of Torsion Theories


Homological And Homotopical Aspects Of Torsion Theories
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Author : Apostolos Beligiannis
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Homological And Homotopical Aspects Of Torsion Theories written by Apostolos Beligiannis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.


In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along these lines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.



Lax Phillips Scattering And Conservative Linear Systems A Cuntz Algebra Multidimensional Setting


Lax Phillips Scattering And Conservative Linear Systems A Cuntz Algebra Multidimensional Setting
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Author : Joseph A. Ball
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Lax Phillips Scattering And Conservative Linear Systems A Cuntz Algebra Multidimensional Setting written by Joseph A. Ball and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Algèbres d'opérateurs categories.


The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. This title presents a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems.



Semigroups Underlying First Order Logic


Semigroups Underlying First Order Logic
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Author : William Craig
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Semigroups Underlying First Order Logic written by William Craig and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Algebraic logic categories.


Boolean, relation-induced, and other operations for dealing with first-order definability Uniform relations between sequences Diagonal relations Uniform diagonal relations and some kinds of bisections or bisectable relations Presentation of ${\mathbf S}_q$, ${\mathbf S}_p$ and related structures Presentation of ${\mathbf S}_{pq}$, ${\mathbf S}_{pe}$ and related structures Appendix. Presentation of ${\mathbf S}_{pqe}$ and related structures Bibliography Index of symbols Index of phrases and subjects List of relations involved in presentations Synopsis of presentations



Equivalences Of Classifying Spaces Completed At The Prime Two


Equivalences Of Classifying Spaces Completed At The Prime Two
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Author : Bob Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Equivalences Of Classifying Spaces Completed At The Prime Two written by Bob Oliver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Classifying spaces categories.


We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.