On centrality of even orthogonal K2

Centrality of odd unitary $K_2$-functor

“…Later in [7,8,11] S. Sinchuk and A. Lavrenov proved similar result for the Chevalley groups of type C l , D l , and E l .…”

Another presentation of orthogonal Steinberg groups

“…He used essentially the same approach: there is another presentation of the symplectic Steinberg group StSp(2l, R) over a commutative ring R for l ≥ 3 such that it is obvious that this group is a central extension of the elementary symplectic group ESp(2l, R). Together with S. Sinchuk he also proved centrality of the corresponding K 2 -functors for Chevalley groups of types D l for l ≥ 3 and E l in [2,5] using a different method.…”

Centrality of $\mathrm K_2$ for Chevalley groups: a pro-group approach

“…The first advancement in the solution of the centrality problem for arbitrary commutative rings since [5] was the counterexample of M. Wendt [33] which showed that the centrality of K 2 may fail for root systems of rank 2 (similarly, there is a counterexample to Suslin's normality theorem for the rank 1 group SL 2 (R)). Soon the papers [9,12,19] of the first-and secondnamed authors appeared, in which it was shown that the centrality of K 2 does, indeed, hold for all the Chevalley groups of type C , D , E provided ≥ 3. In [9] a symplectic analogue of the technique of [5] was developed, while in [12,19] the proof was based on the amalgamation theorem for relative Steinberg groups which reduced the problem of centrality to the alreadyknown linear case.…”

“…Soon the papers [9,12,19] of the first-and secondnamed authors appeared, in which it was shown that the centrality of K 2 does, indeed, hold for all the Chevalley groups of type C , D , E provided ≥ 3. In [9] a symplectic analogue of the technique of [5] was developed, while in [12,19] the proof was based on the amalgamation theorem for relative Steinberg groups which reduced the problem of centrality to the alreadyknown linear case. Nevertheless, neither of these two approaches seemed to work for the root systems B and F 4 .…”