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Relative Nonhomogeneous Koszul Duality
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SYSNO ASEP 0553966 Document Type B - Monograph R&D Document Type Monograph Title Relative Nonhomogeneous Koszul Duality Author(s) Positselski, Leonid (MU-W) SAI, ORCID, RID Issue data Cham: Birkhäuser, 2021 ISBN 978-3-030-89539-6 ISSN 1660-8046 Series Frontiers in Mathematics Number of pages 278 s. Number of copy 500 Publication form Print - P Language eng - English Country CH - Switzerland Issue 1. Keywords relative Koszul duality over a base ring ; coderived and contraderived categories ; D-Omega duality Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA20-13778S GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 EID SCOPUS 85125460851 DOI 10.1007/978-3-030-89540-2 Annotation This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announced in Section 0.4 of [L. Positselski, 'Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures', Monografie Matematyczne IMPAN 70, Springer/Birkhäuser Basel, 2010.] We prove the Poincare-Birkhoff-Witt theorem in this context and construct the triangulated equivalences of derived Koszul duality. The duality between the ring of differential operators and the de Rham DG-algebra, with the ring of functions as the base ring, is the thematic example. The moderate generality level makes the exposition in this book more accessible than the very heavily technical Chapter 11 of ['Homological algebra of semimodules and semicontramodules']. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2022
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