Mathematics – Operator Algebras
Scientific paper
2010-11-28
Mathematics
Operator Algebras
20 pages
Scientific paper
Let ${\Bbb F}_{n}$ 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 $\Delta_{\varphi}$ on $\bigoplus C^{*}({\Bbb F}_{n})$ such that $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$ is a non-cocommutative C$^{*}$-bialgebra, and $C^{*}({\Bbb F}_{\infty})$ is a comodule-C$^{*}$-algebra of $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$. With respect to $\Delta_{\varphi}$, tensor product formulas of several representations of ${\Bbb F}_{n}$'s are computed. From these results, a similarity between $C^{*}({\Bbb F}_{n})$'s and Cuntz algebras are discussed.
No associations
LandOfFree
Non-cocommutative C$^{*}$-bialgebra defined as the direct sum of free group C$^{*}$-algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Non-cocommutative C$^{*}$-bialgebra defined as the direct sum of free group C$^{*}$-algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-cocommutative C$^{*}$-bialgebra defined as the direct sum of free group C$^{*}$-algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-321579