A Primer Of Algebraic D Modules

Author : S. C. Coutinho
Publisher : Cambridge University Press
Page : 223 pages
File Size : 52,8 Mb
Release : 1995-09-07
Category : Mathematics
ISBN : 9780521551199

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A Primer of Algebraic D-Modules by S. C. Coutinho Pdf

The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

Author : Armand Borel
Publisher : Unknown
Page : 382 pages
File Size : 53,6 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:49015000393570

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Algebraic D-modules by Armand Borel Pdf

Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.

Author : Anonim
Publisher : Cambridge University Press
Page : 248 pages
File Size : 44,5 Mb
Release : 2024-06-23
Category : Electronic
ISBN : 8210379456XXX

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Algebraic Theory of Differential Equations by Anonim Pdf

Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 55,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662048511

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Author : Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Publisher : Springer
Page : 258 pages
File Size : 50,8 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319755656

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Commutative Algebra and its Interactions to Algebraic Geometry by Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG Pdf

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.

Author : F. E. A. Johnson
Publisher : Cambridge University Press
Page : 282 pages
File Size : 45,8 Mb
Release : 2003-09-11
Category : Mathematics
ISBN : 0521537495

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Stable Modules and the D(2)-Problem by F. E. A. Johnson Pdf

This 2003 book deals with two fundamental problems in low-dimensional topology with an eye on wider context.

Author : Irena Peeva
Publisher : Springer Science & Business Media
Page : 705 pages
File Size : 42,7 Mb
Release : 2013-02-01
Category : Mathematics
ISBN : 9781461452928

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Commutative Algebra by Irena Peeva Pdf

This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Author : John A. Beachy
Publisher : Cambridge University Press
Page : 252 pages
File Size : 43,8 Mb
Release : 1999-04-22
Category : Mathematics
ISBN : 0521644070

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Introductory Lectures on Rings and Modules by John A. Beachy Pdf

A first-year graduate text or reference for advanced undergraduates on noncommutative aspects of rings and modules.

Author : Joachim Kock
Publisher : Cambridge University Press
Page : 260 pages
File Size : 51,6 Mb
Release : 2004
Category : Mathematics
ISBN : 0521540313

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Frobenius Algebras and 2-D Topological Quantum Field Theories by Joachim Kock Pdf

This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Author : Gert-Martin Greuel,Gerhard Pfister
Publisher : Springer Science & Business Media
Page : 703 pages
File Size : 43,6 Mb
Release : 2007-11-05
Category : Mathematics
ISBN : 9783540735410

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A Singular Introduction to Commutative Algebra by Gert-Martin Greuel,Gerhard Pfister Pdf

This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

Author : G. R. Krause,T. H. Lenagan,T. H Lenagan
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 53,8 Mb
Release : 2000
Category : Associative algebras
ISBN : 9780821808597

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Growth of Algebras and Gelfand-Kirillov Dimension by G. R. Krause,T. H. Lenagan,T. H Lenagan Pdf

During the two decades that preceded the publication of the first edition of this book, the Gelfand-Kirillov dimension had emerged as a very useful and powerful tool for investigating non-commutative algebras. At that time, the basic ideas and results were scattered throughout various journal articles. The first edition of this book provided a much-needed reliable and coherent single source of information. Since that time, the book has become the standard reference source for researchers. For this edition, the authors incorporated the original text with only minor modifications. Errors have been corrected, items have been rephrased, and more mathematical expressions have been displayed for the purpose of clarity. The newly added Chapter 12 provides broad overviews of the new developments that have surfaced in the last few years, with references to the literature for details. The bibliography has been updated and accordingly, almost double the size of the original one. The faithful revision and contemporary design of this work offers time-honored expertise with modern functionality. A keenly appealing combination. So, whether for the classroom, the well-tended mathematical books collection, or the research desk, this book holds unprecedented relevance.

Author : Bruno Buchberger,Franz Winkler
Publisher : Cambridge University Press
Page : 566 pages
File Size : 42,8 Mb
Release : 1998-02-26
Category : Mathematics
ISBN : 0521632986

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Gröbner Bases and Applications by Bruno Buchberger,Franz Winkler Pdf

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 201 pages
File Size : 47,5 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642387425

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Monomial Ideals, Computations and Applications by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Author : Hal Schenck
Publisher : Cambridge University Press
Page : 212 pages
File Size : 55,9 Mb
Release : 2003-10-06
Category : Computers
ISBN : 0521536502

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Computational Algebraic Geometry by Hal Schenck Pdf

The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

Author : Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther
Publisher : American Mathematical Society
Page : 108 pages
File Size : 50,6 Mb
Release : 2022-07-19
Category : Mathematics
ISBN : 9781470471590

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Twenty-Four Hours of Local Cohomology by Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther Pdf

This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.