Lower Central and Dimension Series of Groups PDF Download

Author: Roman Mikhailov
Publisher: Springer Science & Business Media
ISBN: 3540858172
Category : Mathematics
Languages : en
Pages : 367

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Book Description
A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series is a challenging task. This monograph presents an exposition of different methods for investigating this relationship.

Author: Claire Bacha
Publisher: Taylor & Francis
ISBN: 1040066119
Category : Psychology
Languages : en
Pages : 248

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Book Description
The Group Dimension presents a thorough exploration of the history and theory of the group dimension, particularly in the context of modern capitalist society. The book traces the development of capitalism from feudalism, where the first polis groups can be identified, and describes the growth of the power of the state prescribed by John Maynard Keynes to form neoliberalism. Bacha then explores the deep history of human groups, examines how our brains are built for and by multibody interactions and understandings, and provides an overview of our knowledge of groups, building on findings from group analysis. The book concludes by exploring how an understanding of groups, their facilitation and their consciousness redefines current individualistic and autistic 'freedom', to build the new world through dialogue. The Group Dimension will be essential reading for anyone involved in groups, as practitioners or clients. It will also be of interest to readers looking to learn more about groups in the context of modern politics, social and liberation movements.

Author: Fabien Durand
Publisher: Cambridge University Press
ISBN: 1108838685
Category : Mathematics
Languages : en
Pages : 593

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Book Description
This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.

Author: Peter Webb
Publisher: Cambridge University Press
ISBN: 1107162394
Category : Mathematics
Languages : en
Pages : 339

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Book Description
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Author: Alexandru Buium
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 170

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Book Description
Differential algebraic groups were introduced by P. Cassidy and E. Kolchin and are, roughly speaking, groups defined by algebraic differential equations in the same way as algebraic groups are groups defined by algebraic equations. The aim of the book is two-fold: 1) the provide an algebraic geometer's introduction to differential algebraic groups and 2) to provide a structure and classification theory for the finite dimensional ones. The main idea of the approach is to relate this topic to the study of: a) deformations of (not necessarily linear) algebraic groups and b) deformations of their automorphisms. The reader is assumed to possesssome standard knowledge of algebraic geometry but no familiarity with Kolchin's work is necessary. The book is both a research monograph and an introduction to a new topic and thus will be of interest to a wide audience ranging from researchers to graduate students.

Author: Mary Douglas
Publisher: Routledge
ISBN: 1134557507
Category : Social Science
Languages : en
Pages : 360

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Book Description
First published in 1982, this is one of Mary Douglas' favourite books. It is based on her meetings with friends in which they attempt to apply the grip/group analysis from Natural Symbols. The essays have been important texts for preparing grid/group exercises ever since. She is still trying to improve the argument of Natural Symbols and is always hoping to find better applications to illustrate the power of the two dimensions used for accurate comparison.

Author: Piotr Jedrzejowicz
Publisher: Springer
ISBN: 3642239358
Category : Computers
Languages : en
Pages : 658

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Book Description
The two-volume set LNAI 6922 and LNAI 6923 constitutes the refereed proceedings of the Third International Conference on Computational Collective Intelligence, ICCCI 2011, held in Gdynia, Poland, in September 2011. The 112 papers in this two volume set presented together with 3 keynote speeches were carefully reviewed and selected from 300 submissions. The papers are organized in topical sections on knowledge management, machine learning and applications, autonomous and collective decision-making, collective computations and optimization, Web services and semantic Web, social networks and computational swarm intelligence and applications.

Author: Brian Hall
Publisher: Springer
ISBN: 3319134671
Category : Mathematics
Languages : en
Pages : 452

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Book Description
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette

Author: Jim James Yonazi
Publisher: Springer
ISBN: 3642227295
Category : Computers
Languages : en
Pages : 373

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Book Description
This book constitutes the proceedings of the First International Conferences on e-Technologies and Networks for Development, ICeND 2011, held in Dar-es-Salaam, Tanzania, in August 2011. The 29 revised full papers presented were carefully reviewed and selected from 90 initial submissions. The papers address new advances in the internet technologies, networking, e-learning, software applications, Computer Systems, and digital information and data communications technologies - as well technical as practical aspects.

Author: William Eric Davis
Publisher: University Press of America
ISBN: 9780761832485
Category : Biography & Autobiography
Languages : en
Pages : 338

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Book Description
Peace and Prosperity in an Age of Incivility presents a comprehensive theory about peace and prosperity. It asserts that three core political values-liberty, order, and equality- must be allocated by societies through law and policy. This book shows that the optimal allocation is pure balance. Balance of values provides the origin of the "democratic peace," the observation that democracies rarely fight each other and when they do, it is brief, does not escalate, and quickly results in a diplomatic resolution. By building on simple forms of spatial and game theories, this stunning analysis shows that the democratic peace is a "Nash equilibrium," where no player has an incentive to deviate from the solution, given the choices of other "players." Democracy, because it fosters compromise, drives the political values of liberty, order, and equality to intersect in perfect, or at least relative, balance. Maximum peace and prosperity is the consequence of balancing critical values. A nation's level of peace and prosperity, while perhaps not great, will be no greater than when these core values are in balance.