giordano.favi@unibas.ch, emmanuel.lequeu@epfl.ch

Submission: 2004, Dec 22, updated 2005, Feb 25

In these notes we give a criterion for a central simple algebra A to be split in terms of the essential dimension of the algebraic group SL_1(A). This criterion also provides an example of an algebraic group G with ed(G)=n which does not possess any non-trivial cohomological invariant.

2000 Mathematics Subject Classification: 11E72, 16K20

Keywords and Phrases: Central simple algebras, Galois cohomology, essential dimension.

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