Relative Nonhomogeneous Koszul Duality (Paperback, 1st ed. 2021)

This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare-Birkhoff-Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first time in the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Frontiers in Mathematics
Release date:	February 2022
First published:	2021
Authors:	Leonid Positselski
Dimensions:	240 x 168 x 23mm (L x W x T)
Format:	Paperback
Pages:	278
Edition:	1st ed. 2021
ISBN-13:	978-3-03-089539-6
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > General
LSN:	3-03-089539-4
Barcode:	9783030895396

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