On the primary decomposition theorem of modular Lie superalgebras (Q816618)

The authors establish a number of identities for associative Lie superalgebras over a field \(\mathbb{F}\) of characteristic \(p \geq 3\) and some properties of modular Lie superalgebras. They then adapt the proof in Section 1.4 of [\textit{H. Strade} and \textit{R. Farnsteiner}, Modular Lie algebras and their representations. Monographs and Textbooks in Pure and Applied Mathematics, 116, Marcel Dekker, Inc. (1988; Zbl 0648.17003)] for the corresponding Lie algebra result to establish the Primary Decomposition Theorem for nilpotent Lie superalgebras and finite-dimensional \(\mathbb Z_2\)-graded vector spaces over \(\mathbb{F}\).