Strongly self-absorbing  -algebras |
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| Authors: | Andrew S. Toms Wilhelm Winter |
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| Affiliation: | Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 ; Mathematisches Institut der Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany |
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| Abstract: | Say that a separable, unital  -algebra  is strongly self-absorbing if there exists an isomorphism  such that  and  are approximately unitarily equivalent  -homomorphisms. We study this class of algebras, which includes the Cuntz algebras  ,  , the UHF algebras of infinite type, the Jiang-Su algebra  and tensor products of  with UHF algebras of infinite type. Given a strongly self-absorbing  -algebra  we characterise when a separable  -algebra absorbs  tensorially (i.e., is  -stable), and prove closure properties for the class of separable  -stable  -algebras. Finally, we compute the possible  -groups and prove a number of classification results which suggest that the examples listed above are the only strongly self-absorbing  -algebras. |
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| Keywords: | Nuclear $C^*$-algebras K-theory classification |
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