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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

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Volume 27, Issue 5


Semiperfect and coreflexive coalgebras

Sorin Dăscălescu / Miodrag C. Iovanov
  • Facultatea de Matematica, University of Bucharest, Str. Academiei 14, Bucharest 1, RO-010014, Romania; and University of Iowa, MacLean Hall, Iowa City, Iowa 52246, USA
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Published Online: 2013-11-05 | DOI: https://doi.org/10.1515/forum-2013-0085


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 C is isomorphic canonically to the finite dual of its left rational dual Rat (C*C*). 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.

Keywords: Non-unital algebra; semiperfect coalgebra; coreflexive coalgebra; coalgebra; Hopf algebra with non-zero integral

MSC: 16T15; 16T05; 05C38; 06A11; 16T30

About the article

Received: 2013-05-24

Published Online: 2013-11-05

Published in Print: 2015-09-01

Funding Source: UEFISCDI

Award identifier / Grant number: PN-II-ID-PCE-2011-3-0635

Funding Source: CNCSIS

Award identifier / Grant number: 253/5.10.2011

Funding Source: European Social Fund

Award identifier / Grant number: “Postdoctoral program for training scientific researchers”

Funding Source: POSDRU

Award identifier / Grant number: 89/1.5/S/58852

Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2587–2607, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0085.

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