| eBook ISBN: | 978-1-4704-2182-3 |
| Product Code: | ULECT/37.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| eBook ISBN: | 978-1-4704-2182-3 |
| 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–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.
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. Poincaré-Birkhoff-Witt bases
-
Chapter 5. Nonhomogeneous quadratic algebras
-
Chapter 6. Families of quadratic algebras and Hilbert series
-
Chapter 7. Hilbert series of Koszul algebras and one-dependent processes
-
Appendix A. DG-algebras 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
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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–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.
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. Poincaré-Birkhoff-Witt bases
-
Chapter 5. Nonhomogeneous quadratic algebras
-
Chapter 6. Families of quadratic algebras and Hilbert series
-
Chapter 7. Hilbert series of Koszul algebras and one-dependent processes
-
Appendix A. DG-algebras 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
