Path subcoalgebras, finiteness properties and quantum groups

  • Sorin Dăscălescu

    University of Bucharest, Romania
  • Miodrag C. Iovanov

    University of Southern California, Los Angeles, USA
  • Constantin Năstăsescu

    University of Bucharest, Romania


We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach for these classes. We discuss the left quasi-co-Frobenius and the left co-Frobenius properties for these coalgebras. We classify the left co-Frobenius path subcoalgebras, showing that they are direct sums of certain path subcoalgebras arising from the infinite line quiver or from cyclic quivers. We investigate which of the co-Frobenius path subcoalgebras can be endowed with Hopf algebra structures, in order to produce some quantum groups with non-zero integrals, and we classify all these structures over a field with primitive roots of unity of any order. These turn out to be liftings of quantum lines over certain not necessarily abelian groups.

Cite this article

Sorin Dăscălescu, Miodrag C. Iovanov, Constantin Năstăsescu, Path subcoalgebras, finiteness properties and quantum groups. J. Noncommut. Geom. 7 (2013), no. 3, pp. 737–766

DOI 10.4171/JNCG/133