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On Fusion Systems of Component Type

Author : Michael Aschbacher

Publisher : American Mathematical Soc.

Page : 194 pages

File Size : 11,24 MB

Release : 2019-02-21

Category : Mathematics

ISBN : 1470435209

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Book Description

This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups. Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.



Fusion Systems in Algebra and Topology

Author : Michael Aschbacher

Publisher : Cambridge University Press

Page : 329 pages

File Size : 30,4 MB

Release : 2011-08-25

Category : Mathematics

ISBN : 1107601002

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Book Description

A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.





Quaternion Fusion Packets

Author : Michael Aschbacher

Publisher : American Mathematical Soc.

Page : 444 pages

File Size : 47,84 MB

Release : 2021-04-01

Category : Education

ISBN : 1470456656

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Book Description

Let p p be a prime and S S a finite p p-group. A p p-fusion system on S S is a category whose objects are the subgroups of S and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.



Groups St Andrews 2017 in Birmingham

Author : C. M. Campbell

Publisher : Cambridge University Press

Page : 510 pages

File Size : 18,23 MB

Release : 2019-04-11

Category : Mathematics

ISBN : 110872874X

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Book Description

These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.



Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory

Author : Raúl E. Curto

Publisher : American Mathematical Soc.

Page : 112 pages

File Size : 28,56 MB

Release : 2019-09-05

Category : Mathematics

ISBN : 1470436248

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Book Description

In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. The authors then extend the H∞-functional calculus to an H∞¯¯¯¯¯¯¯¯¯+H∞-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of 2×2 partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.



Geometric and Topological Aspects of the Representation Theory of Finite Groups

Author : Jon F. Carlson

Publisher : Springer

Page : 493 pages

File Size : 42,13 MB

Release : 2018-10-04

Category : Mathematics

ISBN : 3319940333

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Book Description

These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.



Multisensor Data Fusion

Author : Hassen Fourati

Publisher : CRC Press

Page : 628 pages

File Size : 47,6 MB

Release : 2017-12-19

Category : Technology & Engineering

ISBN : 1351830880

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Book Description

Multisensor Data Fusion: From Algorithms and Architectural Design to Applications covers the contemporary theory and practice of multisensor data fusion, from fundamental concepts to cutting-edge techniques drawn from a broad array of disciplines. Featuring contributions from the world’s leading data fusion researchers and academicians, this authoritative book: Presents state-of-the-art advances in the design of multisensor data fusion algorithms, addressing issues related to the nature, location, and computational ability of the sensors Describes new materials and achievements in optimal fusion and multisensor filters Discusses the advantages and challenges associated with multisensor data fusion, from extended spatial and temporal coverage to imperfection and diversity in sensor technologies Explores the topology, communication structure, computational resources, fusion level, goals, and optimization of multisensor data fusion system architectures Showcases applications of multisensor data fusion in fields such as medicine, transportation's traffic, defense, and navigation Multisensor Data Fusion: From Algorithms and Architectural Design to Applications is a robust collection of modern multisensor data fusion methodologies. The book instills a deeper understanding of the basics of multisensor data fusion as well as a practical knowledge of the problems that can be faced during its execution.



Compact Quotients of Cahen-Wallach Spaces

Author : Ines Kath

Publisher : American Mathematical Soc.

Page : 96 pages

File Size : 16,35 MB

Release : 2020-02-13

Category : Education

ISBN : 1470441039

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Book Description

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.



A Local Relative Trace Formula for the Ginzburg-Rallis Model: The Geometric Side

Author : Chen Wan

Publisher : American Mathematical Soc.

Page : 102 pages

File Size : 22,75 MB

Release : 2019-12-02

Category : Education

ISBN : 1470436868

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Book Description

Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.