Theory Of Symmetric Lattices

Author : Fumitomo Maeda,Shuichiro Maeda
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642462481

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Theory of Symmetric Lattices by Fumitomo Maeda,Shuichiro Maeda Pdf

Of central importance in this book is the concept of modularity in lattices. A lattice is said to be modular if every pair of its elements is a modular pair. The properties of modular lattices have been carefully investigated by numerous mathematicians, including 1. von Neumann who introduced the important study of continuous geometry. Continu ous geometry is a generalization of projective geometry; the latter is atomistic and discrete dimensional while the former may include a continuous dimensional part. Meanwhile there are many non-modular lattices. Among these there exist some lattices wherein modularity is symmetric, that is, if a pair (a,b) is modular then so is (b,a). These lattices are said to be M-sym metric, and their study forms an extension of the theory of modular lattices. An important example of an M-symmetric lattice arises from affine geometry. Here the lattice of affine sets is upper continuous, atomistic, and has the covering property. Such a lattice, called a matroid lattice, can be shown to be M-symmetric. We have a deep theory of parallelism in an affine matroid lattice, a special kind of matroid lattice. Further more we can show that this lattice has a modular extension.

Author : Lynne M. Butler
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 49,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821826003

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Subgroup Lattices and Symmetric Functions by Lynne M. Butler Pdf

This work presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schutzenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

Author : Peter Crawley,Robert Palmer Dilworth
Publisher : Prentice Hall
Page : 216 pages
File Size : 45,5 Mb
Release : 1973
Category : Mathematics
ISBN : UOM:39015040389127

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Algebraic Theory of Lattices by Peter Crawley,Robert Palmer Dilworth Pdf

Author : Robert Oeckl
Publisher : World Scientific
Page : 216 pages
File Size : 50,7 Mb
Release : 2005-08-22
Category : Science
ISBN : 9781783260171

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Discrete Gauge Theory by Robert Oeckl Pdf

This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork. Contents: Quantization of Discretized Gauge TheoriesTopology: Decomposition of ManifoldsCategories and DiagramsRepresentation Theory: Groups and Hopf AlgebrasCellular Gauge TheoryTopological Quantum Field TheoryRelated ConstructionsApplications to Lattice Models and Quantum Gravity Readership: Researchers in theoretical physics and mathematical physics. Key Features:Extends the discussion with many different models in higher dimensionsProvides a coherent understanding of different subjects and their relations and foundationsMathematically self-contained; the advanced material required is introduced in separate chapters with no prior knowledge of physics necessaryPresents a wide range of cutting-edge applications to quantum gravity and lattice models, not covered in any other bookKeywords:Lattice Gauge Theory;Quantum Groups;Topological Quantum Field Theory (TQFT);Topology;Category Theory;Representation Theory;Quantum GravityReviews:“Both mathematicians and physicists will benefit from this excellent monograph.”Zentralblatt MATH

Author : Garrett Birkhoff
Publisher : Unknown
Page : 244 pages
File Size : 43,7 Mb
Release : 1970
Category : Lattice theory
ISBN : STANFORD:36105033268041

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Trends in Lattice Theory by Garrett Birkhoff Pdf

Author : Anonim
Publisher : Springer-Verlag
Page : 237 pages
File Size : 52,9 Mb
Release : 2013-12-01
Category : Technology & Engineering
ISBN : 9783663124788

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Semimodular Lattices by Anonim Pdf

Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 43,9 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387789019

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Lattices and Ordered Sets by Steven Roman Pdf

This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.

Author : G Kalmbach
Publisher : World Scientific
Page : 240 pages
File Size : 43,7 Mb
Release : 1986-10-01
Category : Hilbert space
ISBN : 9789814531900

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Measures and Hilbert Lattices by G Kalmbach Pdf

Contents: IntroductionOrthomodular MeasuresGleason's TheoremJordan-Hahn DecompositionOrthofacial Sets of StatesEquational Classes Related to StatesDecomposition of Complete Orthomodular LatticesCharacterization of Dimension LatticesBirkhoff-Von Neumann TheoremCoordinatizationsKakutani-Mackey TheoremKeller's Non-Classical Hilbert Spaces Readership: Mathematician and Physicist who are interested in Hilbert Lattices.

Author : Enrico G. Beltrametti,Gianni Cassinelli
Publisher : Cambridge University Press
Page : 340 pages
File Size : 46,9 Mb
Release : 2010-12-09
Category : Mathematics
ISBN : 052116849X

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The Logic of Quantum Mechanics: Volume 15 by Enrico G. Beltrametti,Gianni Cassinelli Pdf

This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.

Author : Anonim
Publisher : Academic Press
Page : 397 pages
File Size : 55,5 Mb
Release : 1978-10-01
Category : Mathematics
ISBN : 9780080873916

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General Lattice Theory by Anonim Pdf

General Lattice Theory

Author : Stephen D. Comer
Publisher : Springer
Page : 290 pages
File Size : 52,9 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540396383

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Universal Algebra and Lattice Theory by Stephen D. Comer Pdf

Author : Library of Congress
Publisher : Unknown
Page : 1544 pages
File Size : 45,5 Mb
Release : 1995
Category : Subject headings, Library of Congress
ISBN : OSU:32435050025527

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Library of Congress Subject Headings by Library of Congress Pdf

Author : Library of Congress. Cataloging Policy and Support Office
Publisher : Unknown
Page : 1512 pages
File Size : 49,6 Mb
Release : 2007
Category : Subject headings, Library of Congress
ISBN : UOM:39015066169619

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Library of Congress Subject Headings by Library of Congress. Cataloging Policy and Support Office Pdf

Author : Library of Congress. Office for Subject Cataloging Policy
Publisher : Unknown
Page : 1352 pages
File Size : 46,9 Mb
Release : 1992
Category : Subject headings, Library of Congress
ISBN : UOM:39015038642149

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Library of Congress Subject Headings by Library of Congress. Office for Subject Cataloging Policy Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512350

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.