On odd unitary Steinberg group

Abstract

Let $R$ be a ring with pseudo-involution, $\mathfrak{L}$ be an odd form parameter, $\mathrm{U}(2n,R,\mathfrak{L})$ be an odd hyperbolic unitary group, $\mathrm{EU}(2n,R,\mathfrak{L})$ be it elementary subgroup and $\mathrm{StU}(2n,R,\mathfrak{L})$ be an odd unitary Steinberg group. We compute the Schur multipliers of $\mathrm{StU}(2n,R,\mathfrak{L})$ and $\mathrm{EU}(R,\mathfrak{L})$.