C^*-bialgebra defined as the direct sum of UHF algebras

2011/09/14 by Kawamura, Katsunori
#16T10 #46K10 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1109.2962

Abstract

Let \cal A₀(*) denote the direct sum of a certain set of UHF algebras and let \cal A(*)≡ \bf C⊕ \cal A₀(*). We introduce a non-cocommutative comultiplication Δ_ϕ on \cal A(*), and give an example of comodule-C^*-algebra of the C^*-bialgebra (\cal A(*),Δ_ϕ). With respect to Δ_ϕ, we define a non-symmetric tensor product of *-representations of UHF algebras and show tensor product formulas of GNS representations by product states.

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