Topic
Comodule
About: Comodule is a research topic. Over the lifetime, 366 publications have been published within this topic receiving 4827 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, the derived categories of DG-modules, DG-comodules, and DG-contramodules are considered, and the equivalence between the latter two categories is established.
Abstract: This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the coderived and contraderived categories of CDG-modules, the coderived categories of CDG-comodules, and the contraderived categories of CDG-contramodules. The equivalence between the latter two categories (the comodule-contramodule correspondence) is established. Nonhomogeneous Koszul duality or "triality" (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 $A_\infty$-structures are considered, and a number of model category structures are described. Homogeneous Koszul duality and $D$-$\Omega$ duality are discussed in the appendices.
286 citations
TL;DR: In this article, the Cleft comodule algebras for a bialgebra have been proposed for the first time, and they have been shown to be a good fit for a Bialgebra.
Abstract: (1986). Cleft comodule algebras for a bialgebra. Communications in Algebra: Vol. 14, No. 5, pp. 801-817.
285 citations
TL;DR: In this paper, the authors examined a variety of algebraic contexts in which the quantum Yang-Baxter equation arises, and derived methods for generating new solutions from given ones, encoded in objects which have a module and a comodule structure over a bialgebra.
273 citations
TL;DR: In this article, the authors introduce quantum group comodule algebras related to the reflection equations, which are quantum group Fq(GL(2)) is taken as the example.
Abstract: Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group Fq(GL(2)) is taken as the example. The properties of the algebras (centre, representation, realizations, real forms, fusion procedure etc) as well as the generalizations are discussed.
236 citations
Book•
24 Jun 2011
TL;DR: In this article, the derived categories of DG-modules, DG-comodules, and DG-contramodules were considered and the equivalence between the latter two categories was established.
Abstract: 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 "triality" (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.
166 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 16 |
| 2020 | 19 |
| 2019 | 14 |
| 2018 | 14 |
| 2017 | 11 |
| 2016 | 14 |