Quadratic Algebras

Quadratic Algebras PDF Author: Alexander Polishchuk
Publisher: American Mathematical Soc.
ISBN: 0821838342
Category : Mathematics
Languages : en
Pages : 176

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Book Description
This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.

Quadratic Algebras

Quadratic Algebras PDF Author: Alexander Polishchuk
Publisher: American Mathematical Soc.
ISBN: 0821838342
Category : Mathematics
Languages : en
Pages : 176

Get Book Here

Book Description
This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups

Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups PDF Author: Alexander J. Hahn
Publisher: Springer Science & Business Media
ISBN: 146846311X
Category : Mathematics
Languages : en
Pages : 296

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Book Description
Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.

Tame Algebras and Integral Quadratic Forms

Tame Algebras and Integral Quadratic Forms PDF Author: Claus M. Ringel
Publisher: Springer
ISBN: 3540391274
Category : Mathematics
Languages : en
Pages : 390

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Book Description


Quadratic Mappings and Clifford Algebras

Quadratic Mappings and Clifford Algebras PDF Author: Jacques Helmstetter
Publisher: Springer Science & Business Media
ISBN: 3764386061
Category : Mathematics
Languages : en
Pages : 512

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Book Description
After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods.

Algebra, Geometry and Mathematical Physics

Algebra, Geometry and Mathematical Physics PDF Author: Abdenacer Makhlouf
Publisher: Springer
ISBN: 3642553613
Category : Mathematics
Languages : en
Pages : 680

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Book Description
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers and advanced students.

NonasSociative Algebra and Its Applications

NonasSociative Algebra and Its Applications PDF Author: R. Costa
Publisher: CRC Press
ISBN: 1482270463
Category : Mathematics
Languages : en
Pages : 488

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Book Description
A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.

Commutative Algebra and Noncommutative Algebraic Geometry

Commutative Algebra and Noncommutative Algebraic Geometry PDF Author: David Eisenbud
Publisher: Cambridge University Press
ISBN: 1107065623
Category : Mathematics
Languages : en
Pages : 463

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Book Description
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Basic Algebra I

Basic Algebra I PDF Author: Nathan Jacobson
Publisher: Courier Corporation
ISBN: 0486135225
Category : Mathematics
Languages : en
Pages : 530

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Book Description
A classic text and standard reference for a generation, this volume covers all undergraduate algebra topics, including groups, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. 1985 edition.

Algebra I

Algebra I PDF Author: N. Bourbaki
Publisher: Springer Science & Business Media
ISBN: 9783540642435
Category : Mathematics
Languages : en
Pages : 750

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Book Description
An exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, and the third investigatesalgebras, particularly tensor algebras.

Computations and Combinatorics in Commutative Algebra

Computations and Combinatorics in Commutative Algebra PDF Author: Anna M. Bigatti
Publisher: Springer
ISBN: 3319513192
Category : Mathematics
Languages : en
Pages : 136

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Book Description
Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.