NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS
Keyword(s):
AbstractLeti ${\Bbb F}$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.
1971 ◽
Vol 5
(1)
◽
pp. 87-94
◽
Keyword(s):
2010 ◽
Vol 54
(1)
◽
pp. 99-111
◽
Keyword(s):
Keyword(s):
1991 ◽
Vol 109
(3)
◽
pp. 521-537
◽
Keyword(s):
1974 ◽
Vol 26
(1)
◽
pp. 185-189
◽
Keyword(s):
1986 ◽
Vol 29
(1)
◽
pp. 97-100
◽
Keyword(s):
1964 ◽
Vol 11
(2)
◽
pp. 205-215
◽
1949 ◽
Vol 1
(2)
◽
pp. 187-190
◽
Keyword(s):
1998 ◽
Vol 41
(2)
◽
pp. 325-332
◽