Lifting formulas. II (Q1574718)

The paper describes a construction for cocycles of a Lie algebra \(A\) that is the Lie algebra of an associative algebra \(A_{\text{ass}}\), provided a set of derivatives \(D_1, \dots,D_n\) is given. Slightly different sets of conditions on the derivatives are discussed. The main application is the Lie algebra of differential operators \(\text{Dif}_n (S^1)\) on \((S^1)^n\). Thus the author constructs cocycles in \(H^k(\text{Dif}_n(S^1), \mathbb{C})\) for \(k=2n+3\), \(2n+5, \dots\), but the question about their nontriviality remains open. The proofs involve quite elaborated calculations and are mostly sketched with details left to the reader. Part I, see Transl. Math. Monogr. 185, 95-110 (1998; Zbl 0928.17024).