Infinitesimal deformations of restricted simple Lie algebras. I (Q2378598)

The second cohomology group with coefficients in the adjoint module of restricted simple Lie algebras of the general (\(W_n\)) and special (\(S_n\)) types is computed. This work was done earlier by \textit{A. Dzhumadil'daev}, but the detailed proofs were not published. The second part of the paper, with a more detailed review [see, J. Pure Appl. Algebra 213, No. 9, 1702--1721 (2009; Zbl 1185.17018)] performs the same task in the remaining cases of contact and Hamiltonian types.