Triangular C${}^{\ast }$-bialgebra defined as the direct sum of matrix algebras

Abstract

Let $M_{\ast }(\mathbf{C})$ denote the C${}^{\ast }$-algebra defined as the direct sum of all matrix algebras $\{M_n(\mathbf{C}):n\ge 1\}$. It is known that $M_{\ast }(\mathbf{C})$ has a non-cocommutative comultiplication ${\Delta }_{\phi }$. We show that the C${}^{\ast }$-bialgebra $(M_{\ast }(\mathbf{C}),{\Delta }_{\phi })$ has a universal $R$-matrix $R$ such that the quasi-cocommutative C${}^{\ast }$-bialgebra $(M_{\ast }(\mathbf{C}),{\Delta }_{\phi },R)$ is triangular.

19 pages

References in corpus (1)

• Non-existence of universal $R$-matrix for some C${}^{\ast }$-bialgebras