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- W4300804913 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 $C$ 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." @default.
- W4300804913 created "2022-10-04" @default.
- W4300804913 creator A5037476567 @default.
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- W4300804913 date "2015-12-31" @default.
- W4300804913 modified "2023-10-17" @default.
- W4300804913 title "Semiperfect and coreflexive coalgebras" @default.
- W4300804913 doi "https://doi.org/10.48550/arxiv.1512.09344" @default.
- W4300804913 hasPublicationYear "2015" @default.
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