On finite basability of some Lie identities systems modulo of Capelli identities (Q1382594)

The author develops the method proposed by \textit{V. V. Stovba} [Vestn. Mosk. Univ., Ser. I 1982, 54-58 (1982; Zbl 0494.17011)]. It is shown that the following systems of identities in Lie algebras are finite basable over the zero characteristics field: the set of all identities containing prescribed numbers of symmetric and skew-symmetric sets of variables of given dimensions; the set of all identities corresponding to Young diagrams containing a fixed \(k\times l\) rectangle with respect to the module of Capelli identities of order \(k+1\).