The Mathematics Of Frobenius In Context
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Author |
: Thomas Hawkins |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 698 |
Release |
: 2013-07-23 |
ISBN-10 |
: 9781461463337 |
ISBN-13 |
: 1461463335 |
Rating |
: 4/5 (37 Downloads) |
Synopsis The Mathematics of Frobenius in Context by : Thomas Hawkins
Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices.
Author |
: Charles W. Curtis |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 308 |
Release |
: 1999 |
ISBN-10 |
: 9780821826775 |
ISBN-13 |
: 0821826778 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer by : Charles W. Curtis
The AMS History of Mathematics series is one of the most popular items for bookstore sales. These books feature colorful, attractive covers that are perfect for face out displays. The topics will appeal to a broad audience in the mathematical and scientific communities.
Author |
: Joachim Kock |
Publisher |
: Cambridge University Press |
Total Pages |
: 260 |
Release |
: 2004 |
ISBN-10 |
: 0521540313 |
ISBN-13 |
: 9780521540315 |
Rating |
: 4/5 (13 Downloads) |
Synopsis Frobenius Algebras and 2-D Topological Quantum Field Theories by : Joachim Kock
This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.
Author |
: Stephen Boyd |
Publisher |
: Cambridge University Press |
Total Pages |
: 477 |
Release |
: 2018-06-07 |
ISBN-10 |
: 9781316518960 |
ISBN-13 |
: 1316518965 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author |
: Thomas Hawkins |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 578 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461212027 |
ISBN-13 |
: 1461212022 |
Rating |
: 4/5 (27 Downloads) |
Synopsis Emergence of the Theory of Lie Groups by : Thomas Hawkins
The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.
Author |
: Bas Lemmens |
Publisher |
: Cambridge University Press |
Total Pages |
: 337 |
Release |
: 2012-05-03 |
ISBN-10 |
: 9780521898812 |
ISBN-13 |
: 0521898811 |
Rating |
: 4/5 (12 Downloads) |
Synopsis Nonlinear Perron-Frobenius Theory by : Bas Lemmens
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Author |
: Matej Brešar |
Publisher |
: Springer |
Total Pages |
: 227 |
Release |
: 2014-10-14 |
ISBN-10 |
: 9783319086934 |
ISBN-13 |
: 3319086936 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Introduction to Noncommutative Algebra by : Matej Brešar
Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.
Author |
: Pavel I. Etingof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 240 |
Release |
: 2011 |
ISBN-10 |
: 9780821853511 |
ISBN-13 |
: 0821853511 |
Rating |
: 4/5 (11 Downloads) |
Synopsis Introduction to Representation Theory by : Pavel I. Etingof
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Author |
: Lluís Puig |
Publisher |
: Birkhäuser |
Total Pages |
: 498 |
Release |
: 2009-08-29 |
ISBN-10 |
: 3034600151 |
ISBN-13 |
: 9783034600156 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Frobenius Categories versus Brauer Blocks by : Lluís Puig
This book contributes to important questions in modern representation theory of finite groups. It introduces and develops the abstract setting of the Frobenius categories and gives the application of the abstract setting to the blocks.
Author |
: Emily Riehl |
Publisher |
: Courier Dover Publications |
Total Pages |
: 273 |
Release |
: 2017-03-09 |
ISBN-10 |
: 9780486820804 |
ISBN-13 |
: 0486820807 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Category Theory in Context by : Emily Riehl
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.