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A criterion for splitting -algebras in tensor products
Authors:  szló  Zsidó  
Institution:Department of Mathematics, University of Rome ``Tor Vergata", Via della Ricerca Scientifica, 00133 Rome, Italy
Abstract:The goal of the paper is to prove the following theorem: if $A$,$D$ are unital $C^{*}$-algebras, $A$ simple and nuclear, then any $C^{*}$-subalgebra of the $C^{*}$-tensor product of $A$ and $D$, which contains the tensor product of $A$ with the scalar multiples of the unit of $D$, splits in the $C^{*}$-tensor product of $A$ with some $C^{*}$-subalgebra of $D$.

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