Journal article
Path subcoalgebras, finiteness properties and quantum groups
Journal of Noncommutative Geometry, Vol.7(3), pp.737-766
2013
DOI: 10.4171/JNCG/133
Abstract
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.
Details
- Title: Subtitle
- Path subcoalgebras, finiteness properties and quantum groups
- Creators
- Sorin Dăscălescu - University of Bucharest, BUCHAREST, ROMANIAMiodrag Iovanov - University of Southern California, LOS ANGELES, UNITED STATESConstantin Năstăsescu - University of Bucharest, BUCHAREST, ROMANIA
- Resource Type
- Journal article
- Publication Details
- Journal of Noncommutative Geometry, Vol.7(3), pp.737-766
- DOI
- 10.4171/JNCG/133
- ISSN
- 1661-6952
- eISSN
- 1661-6960
- Publisher
- European Mathematical Society Publishing House; Zuerich, Switzerland
- Language
- English
- Date published
- 2013
- Academic Unit
- Mathematics
- Record Identifier
- 9983985987502771
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