Journal article
Semiperfect and coreflexive coalgebras
Forum Mathematicum, Vol.27(5), pp.2587-2607
09/01/2015
DOI: 10.1515/forum-2013-0085
Abstract
We study non-counital coalgebras and their dual non-unital algebras, and introduce the finite dual of a non-unital algebra. We show that a theory that parallels in good part the duality in the unital case can be constructed. Using this, we introduce a new notion of left coreflexivity for counital coalgebras, namely, a coalgebra is left coreflexive if is isomorphic canonically to the finite dual of its left rational dual . We show that right semiperfectness for coalgebras is in fact essentially equivalent to this left reflexivity condition, and we give the connection to usual coreflexivity. As application, we give a generalization of some recent results connecting dual objects such as quiver or incidence algebras and coalgebras, and show that Hopf algebras with non-zero integrals (compact quantum groups) are coreflexive.
Details
- Title: Subtitle
- Semiperfect and coreflexive coalgebras
- Creators
- Sorin Dăscălescu - Facultatea de Matematica, University of Bucharest, Str. Academiei 4, Bucharest 1, RO-010014, RomaniaMiodrag C Iovanov - Facultatea de Matematica, University of Bucharest, Str. Academiei 4, Bucharest 1, RO-010014, Romania; and University of Iowa, MacLean Hall, Iowa City, Iowa 2246, USA
- Resource Type
- Journal article
- Publication Details
- Forum Mathematicum, Vol.27(5), pp.2587-2607
- DOI
- 10.1515/forum-2013-0085
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- Publisher
- De Gruyter
- Number of pages
- 21
- Grant note
- 253/5.10.2011 / CNCSIS 89/1.5/S/58852 / POSDRU PN-II-ID-PCE-2011-3-0635 / UEFISCDI “Postdoctoral program for training scientific researchers” / European Social Fund
- Language
- English
- Date published
- 09/01/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985924802771
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