Maslov index and a central extension of the symplectic group. (English) Zbl 1037.11026

Parimala, R.; Preeti, R.; Sridharan, R.

\(K\)-Theory 19, No. 1, 29-45 (2000).

Summary: We show that over any field \(K\) of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to \(I^2(K)\) and that the induced natural homomorphism from \(K_2 \text{Sp}(K)\to I^2(K)\) is indeed the homomorphism given by the symplectic symbol \(\{x,y\}\) mapping to the Pfister form \(\langle 1,-x\rangle \otimes \langle 1,-y\rangle\).
An errata is given in ibid. 19, No. 4, 403 (2000).

MSC:

11E81	Algebraic theory of quadratic forms; Witt groups and rings
19C99	Steinberg groups and \(K_2\)
11E70	\(K\)-theory of quadratic and Hermitian forms

Keywords:

symplectic symbols; Witt group; Pfister form