Cohomology of Restricted Twisted Heisenberg Lie Algebras

Abstract

Over an algebraically closed ffeld F of characteristic p>0, the restricted twisted Heisenberg Lie algebras are studied. We use the Hochschild-Serre spectral sequence relative to its Heisenberg ideal to compute the trivial cohomology. The ordinary 1- and 2-cohomology spaces are used to compute the restricted 1- and 2-cohomology spaces and describe the restricted 1-dimensional central extensions, including explicit formulas for the Lie brackets and [p]-operators.