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Quiver Representations

Quivers
Author: Ralf Schiffler
Publisher: Springer
ISBN: 3319092049
Size: 62.14 MB
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This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
Quiver Representations and Quiver Varieties
Language: en
Pages: 295
Authors: Alexander Kirillov Jr.
Categories: Algebraic geometry -- Cycles and subschemes -- Parametrization (Chow and Hilbert schemes)
Type: BOOK - Published: 2016-08-25 - Publisher: American Mathematical Soc.
This book is an introduction to the theory of quiver representations and quiver varieties, starting with basic definitions and ending with Nakajima's work on quiver varieties and the geometric realization of Kac–Moody Lie algebras. The first part of the book is devoted to the classical theory of quivers of finite type. Here the exposition is mostly self-contained and all important proofs are presented in detail. The second part contains the more recent topics of quiver theory that are related to quivers of infinite type: Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here some of the more technical proofs are omitted; instead only the statements and some ideas of the proofs are given, and the reader is referred to original papers for details. The exposition in the book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the use of this language is reduced to a minimum. The many
Quiver Representations
Language: en
Pages: 230
Authors: Ralf Schiffler
Categories: Mathematics
Type: BOOK - Published: 2014-09-04 - Publisher: Springer
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
The Cone of Effective Weights for Quivers and Horn Type Problems
Language: en
Pages:
Authors: Calin I. Chindris
Categories: Mathematics
Type: BOOK - Published: 2005 - Publisher:
Books about The Cone of Effective Weights for Quivers and Horn Type Problems
Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers
Language: en
Pages: 371
Authors: Kenji Iohara, Philippe Malbos, Masa-Hiko Saito, Nobuki Takayama
Categories: Mathematics
Type: BOOK - Published: 2020-02-20 - Publisher: Springer Nature
This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate
Lie algebras determined by finite Auslander-Reiten quivers
Language: de
Pages: 12
Authors: Liangang Peng
Categories: Mathematics
Type: BOOK - Published: 1994 - Publisher:
Books about Lie algebras determined by finite Auslander-Reiten quivers
North American Bows, Arrows, and Quivers
Language: en
Pages: 49
Authors: Otis T. Mason
Categories: Bow and arrow
Type: BOOK - Published: 1894 - Publisher:
Books about North American Bows, Arrows, and Quivers
Algebras, Quivers and Representations
Language: en
Pages: 298
Authors: Aslak Bakke Buan, Idun Reiten, Øyvind Solberg
Categories: Mathematics
Type: BOOK - Published: 2013-08-24 - Publisher: Springer Science & Business Media
This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulate categories. ​
Algebras whose Auslander-Reiten quivers have large regular components
Language: de
Pages: 28
Authors: William Crawley-Boevey, Claus Michael Ringel
Categories: Mathematics
Type: BOOK - Published: 1990 - Publisher:
Books about Algebras whose Auslander-Reiten quivers have large regular components
Arrows from Two Quivers
Language: en
Pages: 306
Authors: Richard Henderson Rivers, Henry Clay Morrison
Categories: Methodist Church
Type: BOOK - Published: 1890 - Publisher:
Books about Arrows from Two Quivers
When pure love is perverted humanity quivers
Language: en
Pages: 11
Authors: Helena Petrovna Blavatsky
Categories: Religion
Type: BOOK - Published: 2018-07-07 - Publisher: Philaletheians UK
Oh, the unspeakable hypocrisy of our age! The age when everything under the Sun and Moon is for sale and bought. Though centuries lapse and decades of ages drop out of the lap of time, great reforms take place, empires rise and fall and rise again, and even whole races disappear before the triumphant march of civilization, in his terrific selfishness the “man” that was is the “man” that is. In their internal, or rather, essential constitution, both nature and man are at one, as their essence is identical. All grows and develops and strives towards perfection on the former planes of externality or, as well said by a philosopher, is “ever becoming”; but on the ultimate plane of the spiritual essence all is, and remains therefore immutable. It is towards this eternal Esse that everything, as every being, is gravitating gradually, almost imperceptibly, but as surely as the Universe of stars and worlds moves towards a mysterious point known to, yet still unnamed by, astronomy and called by the Occultists — the Central Spiritual Sun. Yet there are still men who, notwithstanding the present chaotic condition of the moral world and the sorry débris of the best human ideals,