0553966 - MÚ 2022 RIV CH eng B - Monography
Positselski, Leonid
Relative Nonhomogeneous Koszul Duality.
1. - Cham: Birkhäuser, 2021. 278 s. Frontiers in Mathematics. ISBN 978-3-030-89539-6. ISSN 1660-8046
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : relative Koszul duality over a base ring * coderived and contraderived categories * D-Omega duality
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-030-89540-2

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'].
Permanent Link: http://hdl.handle.net/11104/0328628