William Fajardo,Claudia Gallego,Oswaldo Lezama,Armando Reyes,Hector Suarez,Helbert Venegas
Skew PBW Extensions: Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications
Skew PBW Extensions: Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications
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Excellent- More about Skew PBW Extensions: Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications
This book explores skew Poincaré-Birkhoff-Witt (PBW) extensions, a new class of non-commutative rings, and investigates finitely generated projective modules over them from a matrix perspective. It develops the theory of Gröbner bases for left and right ideals and modules, computes syzygies and Ext and Tor modules, and applies to noncommutative algebraic geometry of quantum algebras.
Format: Paperback / softback
Length: 584 pages
Publication date: 13 December 2021
Publisher: Springer Nature Switzerland AG
This monograph delves into a novel realm of non-commutative rings, known as skew Poincaré-Birkhoff-Witt (PBW) extensions. It begins with foundational definitions and explores the realm of ring-module theoretic and homological properties, seamlessly transitioning into an investigation of finitely generated projective modules over these extensions from a matrix perspective. To render this theory constructive, the theory of Gröbner bases for left and right ideals and modules for bijective skew PBW extensions is developed. Through this framework, the computation of syzygies and the Ext and Tor modules over these rings is accomplished. Furthermore, the book showcases applications to crucial areas in noncommutative algebraic geometry, encompassing an exploration of semi-graded Koszul algebras and semi-graded Artin-Schelter regular algebras, as well as addressing the noncommutative Zariski cancellation problem. This comprehensive work is intended for researchers in noncommutative algebra and algebraic geometry, as well as for graduate students and advanced undergraduate students seeking to delve into the intricate world of non-commutative mathematics.
Weight: 908g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030533809
Edition number: 1st ed. 2020
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