Tim Wouters: Comparing invariants of SK1


Submission: 2010, Mar 8, revised 2010, Mar 18

In this text, we compare several invariants of the reduced Whitehead group SK1 of a central simple algebra. For biquaternion algebras, we compare a generalised invariant of Suslin as constructed by the author in a previous article to an invariant introduced by Knus-Merkurjev-Rost-Tignol. Using explicit computations, we prove these invariants are essentially the same. We also prove the non-triviality of an invariant introduced by Kahn. To obtain this result, we compare Kahn's invariant to an invariant introduced by Suslin in 1991 which is non-trivial for Platonov's examples of non-trivial SK1. We also give a formula for the value on the centre of the tensor product of two symbol algebras.

2010 Mathematics Subject Classification: 19B99 (12G05, 16K50, 17C20)

Keywords and Phrases: Reduced Whitehead Group -- Suslin's conjecture -- Cohomological invariants -- Symbol algebras

Full text: dvi.gz 77 k, dvi 248 k, ps.gz 901 k, pdf.gz 313 k, pdf 394 k.

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