Описание: Motivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields $K$. A module of a group $G$ over $K$ is imprimitive, if it is induced from a module of a proper subgroup of $G$.The authors obtain their strongest results when ${\rm char}(K) = 0$, although much of their analysis carries over into positive characteristic. If $G$ is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible $KG$-module is Harish-Chandra induced. This being true for $\mbox{\rm char}(K)$ different from the defining characteristic of $G$, the authors specialize to the case ${\rm char}(K) = 0$ and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive $KG$-modules, when $G$ runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to $1$, if the Lie rank of the groups tends to infinity.For exceptional groups $G$ of Lie type of small rank, and for sporadic groups $G$, the authors determine all irreducible imprimitive $KG$-modules for arbitrary characteristic of $K$.
Автор: Schwartz, Richard Evan Название: Spherical cr geometry and dehn surgery ISBN: 0691128103 ISBN-13(EAN): 9780691128108 Издательство: Wiley Рейтинг: Цена: 2816 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proves an analogue of Thurston`s celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. This book is suitable for graduate students interested in this area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.
Автор: Rossi Название: Hilbert Functions of Filtered Modules ISBN: 3642142397 ISBN-13(EAN): 9783642142390 Издательство: Springer Рейтинг: Цена: 3268 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. This title features an extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration.
Автор: Chazal Название: The Structure and Stability of Persistence Modules ISBN: 3319425439 ISBN-13(EAN): 9783319425436 Издательство: Springer Рейтинг: Цена: 4674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
Описание: PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs.Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero.This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.
Автор: Jain, S.K.; Srivastava, Ashish K.; Tuganbaev, Aska Название: Cyclic Modules and the Structure of Rings ISBN: 019966451X ISBN-13(EAN): 9780199664511 Издательство: Oxford Academ Рейтинг: Цена: 7702 р. Наличие на складе: Поставка под заказ.
Описание: This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
Автор: Benoit Fresse Название: Modules over Operads and Functors ISBN: 3540890556 ISBN-13(EAN): 9783540890553 Издательство: Springer Цена: 5325 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The notion of an operad supplies a conceptual and effective device to handle a variety of algebraic structures in various situations. This monograph reviews the basis of operad theory. It studies structures of modules over operads as a device to model functors between categories of algebras as effectively as operads model categories of algebras.
Автор: F. E. A. Johnson Название: Stable Modules and the D(2)-Problem ISBN: 0521537495 ISBN-13(EAN): 9780521537490 Издательство: Cambridge Academ Рейтинг: Цена: 5412 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.
Автор: Brown Martin L. Название: Heegner Modules and Elliptic Curves ISBN: 3540222901 ISBN-13(EAN): 9783540222903 Издательство: Springer Рейтинг: Цена: 7475 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields, this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
Автор: Kashiwara Название: Regular and Irregular Holonomic D-Modules ISBN: 1316613453 ISBN-13(EAN): 9781316613450 Издательство: Cambridge Academ Рейтинг: Цена: 4370 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann–Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Etudes Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.
Автор: Bj?rk Название: Analytic D-Modules and Applications ISBN: 0792321146 ISBN-13(EAN): 9780792321149 Издательство: Springer Цена: 12154 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Aims to provide a complete and systematic treatment of the foundations, together with a thorough discussion of such topics as the Riemann-Hilbert correspondence, Bernstein-Sata polynomials and a large variety of results concerning microdifferential analysis.
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