Varieties Of Groups
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Varieties Of Groups
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Author : Hanna Neumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Varieties Of Groups written by Hanna Neumann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Varieties of algebras are equationally defined classes of algebras, or "primitive classes" in MAL'CEV'S terminology. They made their first explicit appearance in the 1930's, in Garrett BIRKHOFF'S paper on "The structure of abstract algebras" and B. H. NEUMANN'S paper "Identical relations in groups I". For quite some time after this, there is little published evidence that the subject remained alive. In fact, however, as part of "universal algebra", it aroused great interest amongst those who had access, directly or indirectly, to PHILIP HALL'S lectures given at Cambridge late in the 1940's. More recently, category theory has provided a general setting since varieties, suitably interpreted, are very special examples of categories. Whether their relevance to category theory goes beyond this, I do not know. And I doubt that the category theoretical approach to varieties will be more than a fringe benefit to group theory. Whether or not my doubts have substance, the present volume owes its existence not to the fact that varieties fit into a vastly more general pattern, but to the benefit group theory has derived from the classification of groups by varietal properties. It is this aspect of the study of varieties that seems to have caused its reappearance in the literature in the 1950's.
Varieties Of Representations Of Finitely Generated Groups
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Author : Alexander Lubotzky
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Varieties Of Representations Of Finitely Generated Groups written by Alexander Lubotzky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k. The tangent spaces of this variety are subspaces of spaces of one-cocycles and thus the geometry of the variety is locally related to the cohomology of the group. The cohomology is also related to the prounipotent radical of the proalgebraic hull of the group. This paper exploits these two relations to compute dimensions of representation varieties, especially for nilpotent groups and their generalizations. It also presents the foundations of the theory of representation varieties in an expository, self-contained manner.
The Theory Of Classes Of Groups
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Author : Guo Wenbin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Theory Of Classes Of Groups written by Guo Wenbin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.
Topics In Varieties Of Group Representations
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Author : Samuel M. Vovsi
language : en
Publisher: Cambridge University Press
Release Date : 1991-11-28
Topics In Varieties Of Group Representations written by Samuel M. Vovsi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-28 with Mathematics categories.
This book is devoted to the theory of group representations, a young and promising area of modern algebra. It provides a detailed exposition of several central topics in the field, leading to the most current advances and developments. Much of the included material has never been available in book form before. It is intended for a broad audience of researchers and graduate students, working in abstract algebra and its many applications.
Kac Moody Groups Their Flag Varieties And Representation Theory
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Author : Shrawan Kumar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Kac Moody Groups Their Flag Varieties And Representation Theory written by Shrawan Kumar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.
Varieties Of Groups
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Author : Hanna Neumann
language : en
Publisher:
Release Date : 1963
Varieties Of Groups written by Hanna Neumann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Group theory categories.
Representations Of Fundamental Groups Of Algebraic Varieties
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Author : Kang Zuo
language : en
Publisher: Springer
Release Date : 2006-11-14
Representations Of Fundamental Groups Of Algebraic Varieties written by Kang Zuo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Representations Of Fundamental Groups Of Algebraic Varieties
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Author : Kang Zuo
language : en
Publisher:
Release Date : 2014-09-01
Representations Of Fundamental Groups Of Algebraic Varieties written by Kang Zuo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Dominions In Varieties Of Groups
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Author : Arturo Viso Magidin
language : en
Publisher:
Release Date : 1998
Dominions In Varieties Of Groups written by Arturo Viso Magidin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Toroidal Groups
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Author : Yukitaka Abe
language : en
Publisher: Springer
Release Date : 2003-07-01
Toroidal Groups written by Yukitaka Abe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
Toroidal groups are the connecting link between torus groups and any complex Lie groups. Many properties of complex Lie groups such as the pseudoconvexity and cohomology are determined by their maximal toroidal subgroups. Quasi-Abelian varieties are meromorphically separable toroidal groups. They are the natural generalisation of the Abelian varieties. Nevertheless, their behavior can be completely different as the wild groups show.