Frobenius Algebras PDF Download
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| Author | : Joachim Kock |
| Publisher | : Cambridge University Press |
| Total Pages | : 260 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780521540315 |
Download Frobenius Algebras and 2-D Topological Quantum Field Theories Book in PDF, ePub and Kindle
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 | : Andrzej Skowroński |
| Publisher | : European Mathematical Society |
| Total Pages | : 672 |
| Release | : 2011 |
| Genre | : Frobenius algebras |
| ISBN | : 9783037191026 |
Download Frobenius Algebras Book in PDF, ePub and Kindle
This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups, and the finite dimensional Hopf algebras over fields are exhibited. This volume is self contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.
| Author | : Lars Kadison |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821819623 |
Download New Examples of Frobenius Extensions Book in PDF, ePub and Kindle
This volume is based on the author's lecture courses to algebraists at Munich and at Goteborg. He presents a unified approach from the point of view of Frobenius algebras/extensions. The book is intended for graduate students and research mathematicians working in algebra and topology.
| Author | : Michiel Hazewinkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 405 |
| Release | : 2007 |
| Genre | : Modules (Algebra) |
| ISBN | : 1402051409 |
Download Algebras, Rings and Modules Book in PDF, ePub and Kindle
| Author | : George Janelidze, Bodo Pareigis, and Walter Tholen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 588 |
| Release | : |
| Genre | : |
| ISBN | : 9780821871478 |
Download Galois Theory, Hopf Algebras, and Semiabelian Categories Book in PDF, ePub and Kindle
| Author | : Thomas Hawkins |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 698 |
| Release | : 2013-07-23 |
| Genre | : Mathematics |
| ISBN | : 1461463335 |
Download The Mathematics of Frobenius in Context Book in PDF, ePub and Kindle
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 | : Stefaan Caenepeel |
| Publisher | : Springer |
| Total Pages | : 359 |
| Release | : 2004-10-13 |
| Genre | : Mathematics |
| ISBN | : 3540480420 |
Download Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations Book in PDF, ePub and Kindle
Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.
| Author | : Jorge L. Ramírez Alfonsín |
| Publisher | : OUP Oxford |
| Total Pages | : 260 |
| Release | : 2005-12-01 |
| Genre | : Mathematics |
| ISBN | : 0191524484 |
Download The Diophantine Frobenius Problem Book in PDF, ePub and Kindle
During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, . At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
| Author | : Ronald Harold Wenger |
| Publisher | : |
| Total Pages | : 152 |
| Release | : 1965 |
| Genre | : Algebra |
| ISBN | : |
Download Semigroups Having Quasi-frobenius Algebras Book in PDF, ePub and Kindle
| Author | : Gregory Karpilovsky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 381 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9400905971 |
Download Symmetric and G-algebras Book in PDF, ePub and Kindle
The theory of symmetric and G-algebras has experienced a rapid growth in the last ten to fifteen years, acquiring mathematical depth and significance and leading to new insights in group representation theory. This volume provides a systematic account of the theory together with a number of applicat
