Semiperfect and coreflexive coalgebras
| Autor: | Dascalescu, Sorin, Iovanov, Miodrag C. |
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| Rok vydání: | 2015 |
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| Zdroj: | Forum Math. 27 (2015), No. 5, 2587--2608 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 14pp; published version 22pp |
| Databáze: | arXiv |
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