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

2008/01/30 by Kawamura, Katsunori
#16W30 #81T05 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0801.4597

Abstract

Let \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_*⊗ \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.

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