Koszul pairs and applications

  • Pascual Jara

    Universidad de Granada, Spain
  • Javier López Peña

    University College London, UK
  • Dragoş Ştefan

    University of Bucharest, Romania


Let be a semisimple ring. A pair is called almost-Koszul if is a connected graded -ring and is a compatible connected graded -coring. To an almost-Koszul pair one associates three chain complexes and three cochain complexes such that one of them is exact if and only if the others are so. In this situation is said to be Koszul. One proves that a connected -ring is Koszul if and only if there is a connected -coring such that is Koszul. This result allows us to investigate the Hochschild (co)homology of Koszul rings. We apply our method to show that the twisted tensor product of two Koszul rings is Koszul. More examples and applications of Koszul pairs, including a generalization of Fröberg Theorem [12], are discussed in the last part of the paper.

Cite this article

Pascual Jara, Javier López Peña, Dragoş Ştefan, Koszul pairs and applications. J. Noncommut. Geom. 11 (2017), no. 4, pp. 1289–1350

DOI 10.4171/JNCG/11-4-3