A local-global principle for symplectic $\mathrm K_2$

Abstract

We prove that an element of the symplectic Steinberg group is trivial if and only if its image under any maximal localisation homomorphism is trivial.

On centrality of even orthogonal $\mathrm K_2$

“…In rank 2 there are known counterxamples to centrality of K 2 , which shows that our assumption on the rank of Φ in theorem 2 is the best possible, see [11]. We also note that recently the first-named author has obtained an analogue of theorem 2 for K 2 (C ℓ , R) under the assumption ℓ ≥ 3, see [12].…”