Computation of cohomology groups of the Lie algebras of type \(B_n\) and \(C_n\)
This short note announces the implementation of a computer package to compute the second cohomology group of classical Lie algebras of type \(B_n\), \(C_n\) over a field of characteristic \(p=2\). For the orthogonal case, it is shown that for ranks \(3\leq n\leq 7\) the cohomology group \(H^2(L,L)\) vanishes, up to the case of \(n=4\), which is of dimension \(16\). The basis of cocycles is given. For the \(C_n\) case, it is shown that for ranks \(3\leq n\leq 8\) the cohomology group has dimension \(2n^2+5n-1\). This confirms previous examples in the literature indicating that the rigidity properties of classical algebras do not generally extend to positive characteristic.
scientific article; zbMATH DE number 5633033