Comparing Invariants of SK1 |
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Authors: | Tim Wouters |
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Institution: | 1. Departement Wiskunde, K.U.Leuven, Celestijnenlaan 200B bus 2400, 3001, Leuven, Belgium
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Abstract: | In this text, we compare an invariant of the reduced Whitehead group SK 1 of a central simple algebra recently introduced by Kahn (2010) to other invariants of SK 1. Doing so, we prove the non-triviality of Kahn’s invariant using the non-triviality of an invariant introduced by Suslin (1991) which is non-trivial for Platonov’s examples of non-trivial SK 1 (Platonov, Math USSR Izv 10(2):211–243, 1976). We also give a formula for the value on the centre of the tensor product of two symbol algebras which generalises a formula of Merkurjev for biquaternion algebras (Merkurjev 1995). |
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