Series: Springer Monographs in Mathematics
1st Edition., 2011, XVI, 476 p. 15 illus., Hardcover
ISBN: 978-0-85729-159-2
Due: September 30, 2010
The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-contained manner. Topics include the structure of Verma modules and Fock modules, the classification of (unitarizable) Harish-Chandra modules, tilting equivalence, and the rational vertex operator algebras associated to the so-called minimal series representations.
Covering a wide range of material, this book has three appendices which provide background information required for some of the chapters. Fundamental results are organized in a unified way and existing proofs refined. For instance in chapter three, a generalization of Jantzen filtration is reformulated in an algebraic manner, and geometric interpretation is provided. Statements, widely believed to be true, are collated, and results which are known but not verified are proven, such as the corrected structure theorem of Fock
modules in chapter eight.
Preliminary.- Classification of Harish-Chandra Modules.- The Jantzen Filtration.- Determinant Formulae.- Verma Modules I: Preliminaries.- Verma Modules II: Structure Theorem.- A Duality among Verma Modules.- Fock Modules.- Rational Vertex Operator Algebras.- Coset Constructions for sl2.- Unitarisable Harish-Chandra Modules.- Homological Algebras.- Lie p-algebras.- Vertex Operator Algebras.
Series: Applied Logic Series, Vol. 37
1st Edition., 2011, V, 240 p., Hardcover
ISBN: 978-94-007-0001-7
Due: November 2010
This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).
Preface,.- 1 Introduction to Hybrid Logic.- 2 Proof-Theory of Propositional Hybrid Logic .- 3 Tableaus and Decision Procedures for Hybrid Logic .- 4 Comparison to Seligman’s Natural Deduction System .- 5 Functional Completeness for a Hybrid Logic .- 6 First-Order Hybrid.- 7 Intensional First-Order Hybrid Logic.- 8 Intuitionistic Hybrid Logic.- 9 Labelled Versus Internalized Natural Deduction .- 10 Why does the Proof-Theory of Hybrid Logic Behave soWell? - References .- Index.
Series: Monografie Matematyczne, Vol. 71
1st Edition., 2011, XII, 534 p., Hardcover
ISBN: 978-3-0348-0005-1
Due: November 15, 2010
Study of the real line taking into account recent results of set theory
Self-contained, all necessary results being revisited
Includes appendix with concise explanation of the metamathematics behind set theory
Exercises with additional results at the end of each section
The rapid development of set theory in the last fifty years, mainly in obtaining plenty of independence results, strongly influenced an understanding of the structure of the real line. This book is devoted to the study of the real line and its subsets taking into account the recent results of set theory. Whenever possible the presentation is done without the full axiom of choice. Since the book is intended to be self-contained, all necessary results of set theory, topology, measure theory, descriptive set theory are revisited with the purpose to eliminate superfluous use of an axiom of choice. The duality of measure and category is studied in a detailed manner. Several statements pertaining to properties of the real line are shown to be undecidable in set theory. The metamathematics behind it is shortly explained in the appendix. Each section contains a series of exercises with additional results.
Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.
Series: Operator Theory: Advances and Applications, Vol. 211
Subseries: Advances in Partial Differential Equations
1st Edition., 2011, VIII, 346 p., Hardcover
ISBN: 978-3-0348-0023-5
November 2010
This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear, expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.
Preface.- L. Chen, M. Dreher: Quantum semiconductor models.- H. Bel Hadj Ali, A. Ben Amor, J. Brasche: Large coupling convergence: Overview and new results.- M. Ben-Artzi: Smooth spectral calculus.- W. Bauer, K. Furutani, C. Iwasaki: Spectral analysis and geometry of sub-Laplacian and related Grushin-type operators.- G. Mendoza: Zeta functions of elliptic cone operators.- P. McKeag, Y. Safarov: Pseudodifferential operators on manifolds: A coordinate-free approach.
Series: Graduate Texts in Mathematics, Vol. 260
1st Edition., 2011, XIV, 305 p. 5 illus., Hardcover
ISBN: 978-0-85729-105-9
Due: October 2010
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals.
Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Grobner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions and resolutions and some of the combinatorics related to monomial ideals including the Kruskal?Katona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing a valuable overview of some of the central trends in algebraic combinatorics.
Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory is complemented by a number of examples and exercises throughout, bringing the reader to a deeper understanding of concepts explored within the text.
Self-contained and concise, this book will appeal to a wide range of readers, including PhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowledge of commutative algebra.
Since their first meeting in 1985, Juergen Herzog (Universitat Duisburg-Essen, Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in this monograph.
Part I Grobner bases: Monomial Ideals.- A short introduction to Grobner bases.- Monomial orders and weights.- Generic initial ideals.- The exterior algebra.- Part II: Hilbert functions and resolutions.- Hilbert functions and the theorems of Macaulay and Kruskal-Katona.- Resolutions of monomial ideals and the Eliahou-Kervaire formula.- Alexander duality and resolutions.- Part III Combinatorics: Alexander duality and finite graphs.- Powers of monomial ideals.- Shifting theory.- Discrete Polymatroids.- Some homological algebra.- Geometry
Collection: Progress in Mathematics, Vol. 286
1st Edition., 2011, Env. 495 p., Relie
ISBN: 978-3-0348-0011-2
November 30, 2010
La geometrie rigide est devenue, au fil des ans, un outil indispensable dans un grand nombre de questions en geometrie arithmetique. Depuis ses premieres fondations, posees par J. Tate en 1961, la theorie s’est developpee dans des directions variees. Ce livre est le premier volume d’un traite qui expose un developpement systematique de la geometrie rigide suivant l’approche de M. Raynaud, basee sur les schemas formels a eclatements admissibles pres. Ce volume est consacre a la construction des espaces rigides dans une situation relative et a l’etude de leurs proprietes geometriques. L’accent est particulierement mis sur l’etude de la topologie admissible d’un espace rigide coherent, analogue de la topologie de Zariski d’un schema. Parmi les sujets traites figurent l’etude des faisceaux coherents et de leur cohomologie, le theoreme de platification par eclatements admissibles qui generalise au cadre formel-rigide un theoreme de Raynaud-Gruson dans le cadre algebrique, et le theoreme de comparaison du type GAGA pour les faisceaux coherents. Ce volume contient aussi de larges rappels et complements de la theorie des schemas formels de Grothendieck. Ce traite est destine tout autant aux etudiants ayant une bonne connaissance de la geometrie algebrique et souhaitant apprendre la geometrie rigide qu’aux experts en geometrie algebrique et en theorie des nombres comme source de references.