NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS

KAWAMURA, KATSUNORI

Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 119-136

Résumé

Leti ${\Bbb F}$n be the free group of rank n and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C*-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n} (1\leq n<\infty$). We introduce a new comultiplication Δφ on $\bigoplus C^{*}({\Bbb F}_{n})$ such that $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$ is a non-cocommutative C*-bialgebra. With respect to Δφ, the tensor product π⊗φπ′ of any two representations π and π′ of free groups is defined. The operation ×φ is associative and non-commutative. We compute its tensor product formulas of several representations.

Détail

DOI : 10.1017/S0017089515000099

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