eBook ISBN:  9781470421823 
Product Code:  ULECT/37.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470421823 
Product Code:  ULECT/37.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 

Book DetailsUniversity Lecture SeriesVolume: 37; 2005; 159 ppMSC: Primary 16; 13; 60
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, noncommutative geometry, \(K\)theory, number theory, and noncommutative linear algebra.
The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincaré–Birkhoff–Witttype 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 onedependent discretetime stochastic processes.
The book can be used by graduate students and researchers working in algebra and any of the abovementioned areas of mathematics.
ReadershipGraduate students and research mathematicians interested in algebra.

Table of Contents

Chapters

Chapter 1. Preliminaries

Chapter 2. Koszul algebras and modules

Chapter 3. Operations on graded algebras and modules

Chapter 4. PoincaréBirkhoffWitt bases

Chapter 5. Nonhomogeneous quadratic algebras

Chapter 6. Families of quadratic algebras and Hilbert series

Chapter 7. Hilbert series of Koszul algebras and onedependent processes

Appendix A. DGalgebras and Massey products


Additional Material

Reviews

The authors are leading experts in the field, and the book is a rather complete statement of the art of these subjects. Many known results are unified and generalized. The book is recommended to anybody interested in these subjects.
Mathematical Reviews


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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, noncommutative geometry, \(K\)theory, number theory, and noncommutative linear algebra.
The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincaré–Birkhoff–Witttype 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 onedependent discretetime stochastic processes.
The book can be used by graduate students and researchers working in algebra and any of the abovementioned areas of mathematics.
Graduate students and research mathematicians interested in algebra.

Chapters

Chapter 1. Preliminaries

Chapter 2. Koszul algebras and modules

Chapter 3. Operations on graded algebras and modules

Chapter 4. PoincaréBirkhoffWitt bases

Chapter 5. Nonhomogeneous quadratic algebras

Chapter 6. Families of quadratic algebras and Hilbert series

Chapter 7. Hilbert series of Koszul algebras and onedependent processes

Appendix A. DGalgebras and Massey products

The authors are leading experts in the field, and the book is a rather complete statement of the art of these subjects. Many known results are unified and generalized. The book is recommended to anybody interested in these subjects.
Mathematical Reviews