Two Kinds of Derived Categories, Koszul Duality, and Comodule-Contramodule Correspondence (eBook)

Leonid Positselski (Autor)

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133 Seiten
American Mathematical Society (Verlag)
978-1-4704-0613-4 (ISBN)

Infos

The aim of this paper is to construct the derived nonhomogeneous Koszul duality. The author considers the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived categories of CDG-modules, the coderived category of CDG-comodules, and the contraderived category of CDG-contramodules. The equivalence between the latter two categories (the comodule-contramodule correspondence) is established. Nonhomogeneous Koszul duality or "e;triality"e; (an equivalence between exotic derived categories corresponding to Koszul dual (C)DG-algebra and CDG-coalgebra) is obtained in the conilpotent and nonconilpotent versions. Various A-infinity structures are considered, and a number of model category structures are described. Homogeneous Koszul duality and D-$/Omega$ duality are discussed in the appendices.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 1-4704-0613-6 / 1470406136
• ISBN-13: 978-1-4704-0613-4 / 9781470406134