7 C ∗ - bialgebra defined by the direct sum of Cuntz algebras ( The revised )
نویسنده
چکیده
We show that a tensor product among representation of certain C∗-algebras induces a bialgebra. Let Õ∗ be the smallest unitization of the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . We show that there exists a non-cocommutative comultiplication ∆ and a counit ε of Õ∗. From ∆, ε and the standard algebraic structure, Õ∗ is a C ∗-bialgebra. Furthermore we show the following: (i) The antipode on Õ∗ never exist. (ii) There exists a unique Haar state on Õ∗. (iii) For a certain one-parameter bialgebra automorphism group of Õ∗, a KMS state on Õ∗ exists. Mathematics Subject Classifications (2000). 47L55, 81T05.
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