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| Author | : Byoung-Song Chwe |
| Publisher | : |
| Total Pages | : 82 |
| Release | : 1961 |
| Genre | : Algebra, Abstract |
| ISBN | : |
| Author | : Leonid Positselski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 364 |
| Release | : 2010-09-02 |
| Genre | : Mathematics |
| ISBN | : 303460436X |
This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.
| Author | : Edgar E. Enochs |
| Publisher | : Walter de Gruyter |
| Total Pages | : 377 |
| Release | : 2011-10-27 |
| Genre | : Mathematics |
| ISBN | : 3110215217 |
This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.
| Author | : Charles A. Weibel |
| Publisher | : Cambridge University Press |
| Total Pages | : 470 |
| Release | : 1995-10-27 |
| Genre | : Mathematics |
| ISBN | : 113964307X |
The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
| Author | : Samuel Eilenberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 43 |
| Release | : 1965 |
| Genre | : Algebra, Homological |
| ISBN | : 0821812556 |
The main notion of this paper is that of a "projective class of sequences" in an arbitrary (pointed) category. Each such class carries with it its own projective objects. One can then talk about projective resolutions, and if the category is additive, all the usual properties of the resolutions hold. In particular, this will permit the development of homological algebra in some additive categories which are not abelian, e.g., the category of comodules over a coalgebra over an arbitrary commutative ring.
| Author | : Edgar E. Enochs |
| Publisher | : Walter de Gruyter |
| Total Pages | : 109 |
| Release | : 2011-08-29 |
| Genre | : Mathematics |
| ISBN | : 3110215233 |
This second volume deals with the relative homological algebra of complexes of modules and their applications. It is a concrete and easy introduction to the kind of homological algebra which has been developed in the last 50 years. The book serves as a bridge between the traditional texts on homological algebra and more advanced topics such as triangulated and derived categories or model category structures. It addresses to readers who have had a course in classical homological algebra, as well as to researchers.
| Author | : Henri Cartan |
| Publisher | : Princeton University Press |
| Total Pages | : 410 |
| Release | : 1999-12-19 |
| Genre | : Mathematics |
| ISBN | : 9780691049915 |
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.
| Author | : Samuel Eilenberg |
| Publisher | : |
| Total Pages | : |
| Release | : 1965 |
| Genre | : |
| ISBN | : |
| Author | : Ivan Penkov |
| Publisher | : Springer Nature |
| Total Pages | : 245 |
| Release | : 2022-01-05 |
| Genre | : Mathematics |
| ISBN | : 3030896609 |
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
| Author | : Anthony W. Knapp |
| Publisher | : Princeton University Press |
| Total Pages | : 526 |
| Release | : 1988-05-21 |
| Genre | : Mathematics |
| ISBN | : 9780691084985 |
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and Lie theory. These notes develop what is needed beyond a first graduate course in algebra in order to appreciate cohomological induction and to see its first consequences. Along the way one is able to study homological algebra with a significant application in mind; consequently one sees just what results in that subject are fundamental and what results are minor.
