Restricted Cohomology of Heisenberg Lie Algebras

The Heisenberg Lie algebras over an algebraically closed field F of characteristic p > 0 always admit a family of restricted Lie algebras. We use the ordinary 1- and 2-cohomology spaces with adjoint coefficients to compute the restricted 1- and 2-cohomology spaces of these restricted Heisenberg Lie algebras. We describe the infinitesimal restricted deformations of the restricted Lie algebras.
Comment: arXiv admin note: text overlap with arXiv:2402.14249. arXiv admin note: text overlap with arXiv:2402.14249