C∗-bialgebra defined by the direct sum of Cuntz algebras

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C-bialgebra defined by the direct sum of Cuntz algebras

Katsunori Kawamura1 College of Science and Engineering Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577,Japan Abstract We show that there exists a non-cocommutative comultiplication ∆φ and a counit ε on the direct sum of Cuntz algebras O∗ ≡ C⊕O2 ⊕O3 ⊕O4 ⊕ · · · . From ∆φ, ε and the standard algebraic structure, the C ∗-algebra O∗ is a bialgebra. Furthermore we show the follow...

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7 C ∗ - bialgebra defined by the direct sum of Cuntz algebras ( The revised )

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 an...

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

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 repr...

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Algebras defined by homomorphisms

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

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ژورنال

عنوان ژورنال: Journal of Algebra

سال: 2008

ISSN: 0021-8693

DOI: 10.1016/j.jalgebra.2008.01.037