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edited Nov 2, 2015 at 6:52

Connectivity of group of invertible elements in $C(S^{2})\otimes A$

For what type of $C^{*}$ algebras $A$, the group of invertible elements of $C(S^{2}) \otimes A$ is a connected group?

All finite dimensional $A$ satisfy this property.

Is it true to say that $A$ satisfy the above property if and only if the group of invertible elements of $A$ is connected?

asked Nov 2, 2015 at 6:05