A Cayley–Hamilton Theorem for the Skew Capelli Elements

For the central elements of the universal enveloping algebra of the Lie algebra n named “the skew Capelli elements,” a Cayley–Hamilton type formula is given. Its classical counterpart is an elementary formula for two alternating matrices. As a byproduct of the main result, the description of the skew Capelli elements given by K. Kinoshita and M. Wakayama (Explicit Capelli identities for skew symmetric matrices, Proc. Edinburgh Math. Soc., to appear) is deduced naturally.