Relative Nonhomogeneous Koszul Duality

The theory of relative nonhomogeneous Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, and this book provides a comprehensive treatment of it, including homogeneous and nonhomogeneous quadratic duality, the Poincare-Birkhoff-Witt theorem, and triangulated equivalences. The thematic example of the classical duality between differential operators and de Rham DG algebra is discussed, and derived D-Omega duality is included in a general framework.

Format: Paperback / softback
Length: 278 pages
Publication date: 11 February 2022
Publisher: Springer Nature Switzerland AG

This comprehensive research monograph delves into the intricate theory of relative nonhomogeneous Koszul duality, a fundamental phenomenon in the realm of homological algebra and its related fields. Koszul duality holds significant importance in algebraic topology, algebraic geometry, and representation theory, serving as a cornerstone of modern mathematical research. With its wide-ranging applications, Koszul duality continues to captivate the attention of scholars worldwide.

This book, authored by a renowned expert in the field, presents a comprehensive exploration of both homogeneous and nonhomogeneous quadratic duality theories over nonsemisimple, noncommutative base rings. It further extends the Poincare-Birkhoff-Witt theorem to this context and establishes triangulated equivalences between various exotic derived categories of modules, curved DG comodules, and curved DG contramodules. A notable example discussed in detail is the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, which involves some of the most crucial objects of study in contemporary algebraic and differential geometry.

For the first time in the history of Koszul duality, this research monograph incorporates the derived D-Omega duality into a general framework. Numerous examples, particularly relevant to algebraic and differential geometry, are analyzed in depth, providing valuable insights into the subject matter.

In conclusion, this research monograph is a vital contribution to the field of homological algebra and its interdisciplinary applications. By presenting a comprehensive treatment of relative nonhomogeneous Koszul duality, it offers a deep understanding of this fundamental phenomenon and its applications to various branches of mathematics. It serves as a valuable resource for both researchers and students alike, paving the way for further advancements in this dynamic and rapidly evolving area of study.

Weight: 536g
Dimension: 168 x 239 x 23 (mm)
ISBN-13: 9783030895396
Edition number: 1st ed. 2021