C$^{*}$-bialgebra defined by the direct sum of Cuntz-Krieger algebras

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dc.creatorKawamura, Katsunori
dc.date2008-01-30
dc.date2008-04-10
dc.date.accessioned2026-07-07T09:31:14Z
dc.date.available2026-07-07T09:31:14Z
dc.descriptionLet ${\sf CK}_{*}$ denote the C$^{*}$-algebra defined by the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication $Δ_ϕ$ and a counit $ε$ on ${\sf CK}_{*}$ such that $Δ_ϕ$ is a nondegenerate $*$-homomorphism from ${\sf CK}_{*}$ to ${\sf CK}_{*}\otimes {\sf CK}_{*}$ and $ε$ is a $*$-homomorphism from ${\sf CK}_{*}$ to ${\bf C}$. From this, ${\sf CK}_{*}$ is a counital non-commutative non-cocommutative C$^{*}$-bialgebra. Furthermore, C$^{*}$-bialgebra automorphisms, a tensor product of representations and C$^{*}$-subbialgebras of ${\sf CK}_{*}$ are investigated.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0801.4597
dc.identifierhttp://arxiv.org/abs/0801.4597
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158386
dc.subjectOperator Algebras
dc.subjectQuantum Algebra
dc.subject16W30; 81T05
dc.titleC$^{*}$-bialgebra defined by the direct sum of Cuntz-Krieger algebras
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