Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite=dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and iterated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial...
Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years re...
Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years the relationship between model theory and other branches of mathematics has led to many profound and intriguing results. This self-contained introduction to the subject introduces the requisite model theory and module theory as it is needed. It then develops the basic ideas of determining what can be said about modules using the information that may be expressed in first-order language. Later chapters discuss stability-theoretic aspects of...
Professor Prest is the first to address the topic of the development of the interplay between model theory and the theory of modules. In recent years ...
The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.
The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theor...
This volume is an outgrowth of the LMS Durham Symposium on L-functions, held in July 1989. The Symposium consisted of several short courses, aimed at presenting rigorous but nontechnical explanations of the latest research areas, and a number of individual lectures on specific topics.
This volume is an outgrowth of the LMS Durham Symposium on L-functions, held in July 1989. The Symposium consisted of several short courses, aimed at ...
The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given...
The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably...
Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarized higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes sketched in when the details are not essential for understanding the key...
Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of s...
The role of representation theory in algebra is an important one and in this book Manz and Wolf concentrate on that part of the theory that relates to solvable groups. In particular, modules over finite fields are studied, but also some applications to ordinary and Brauer characters of solvable groups are given. The authors include a proof of Brauer's height-zero conjecture and a new proof of Huppert's classification of 2-transitive solvable permutation groups.
The role of representation theory in algebra is an important one and in this book Manz and Wolf concentrate on that part of the theory that relates to...
This volume reflects the progress made in many branches of recent research in Banach space theory, an analytic approach to geometry. Including papers by most of the leading figures in the area, it is intended to illustrate the interplay of Banach space theory with harmonic analysis, probability, complex function theory, and finite dimensional convexity theory. The papers consist of a selection of surveys and original research.
This volume reflects the progress made in many branches of recent research in Banach space theory, an analytic approach to geometry. Including papers ...
