NonstableK-Theory for operator algebras |
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Authors: | Klaus Thomsen |
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Institution: | (1) Matematisk Institut, Aarhus Universitet, Ny Munkegade, 8000 Aarhus C, Denmark |
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Abstract: | We show that the homotopy groups of the group of quasi-unitaries inC
*-algebras form a homology theory on the category of allC
*-algebras which becomes topologicalK-theory when stabilized. We then show how this functorial setting, in particular the half-exactness of the involved functors, helps to calculate the homotopy groups of the group of unitaries in a series ofC
*-algebras. The calculations include the case of all AbelianC
*-algebras and allC
*-algebras of the formAB, whereA is one of the Cuntz algebras On n=2, 3, ..., an infinite dimensional simpleAF-algebra, the stable multiplier or corona algebra of a-unitalC
*-algebra, a properly infinite von Neumann algebra, or one of the projectionless simpleC
*-algebras constructed by Blackadar. |
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Keywords: | C
*-algebras homotopy groups unitary groups homology theory |
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