C-bialgebra defined by the direct sum of Cuntz-Krieger algebras
نویسنده
چکیده
Let CK∗ denote the C ∗-algebra defined by the direct sum of all Cuntz-Krieger algebras. We introduce a comultiplication ∆φ and a counit ε on CK∗ such that ∆φ is a nondegenerate ∗-homomorphism from CK∗ to CK∗ ⊗ CK∗ and ε is a ∗-homomorphism from CK∗ to C. From this, CK∗ is a counital non-commutative non-cocommutative C ∗bialgebra. Furthermore, C∗-bialgebra automorphisms, a tensor product of representations and C∗-subbialgebras of CK∗ are investigated. Mathematics Subject Classifications (2000). 16W30, 81T05.
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