Lie superhomomorphisms on Lie ideals in superalgebras (Q375897)

In this paper the author investigates Lie superhomomorphisms from a Lie ideal of the skew elements of a superalgebra with superinvolution into a unital superalgebra. As a consequence a well-known result on Lie isomorphisms [\textit{K. I. Beidar} et al., Trans. Am. Math. Soc. 353, No. 10, 4235--4260 (2001; Zbl 1019.16019) (Theorem 3.5)]; [\textit{M. Brešar} et al., Functional identities. Frontiers in Mathematics. Basel: Birkhäuser (2007; Zbl 1132.16001) (Theorem 6.18)] is improved by reducing the 9-free assumption to the 6-free assumption. Similarly, the problem of Lie superhomomorphisms on Lie ideals of superalgebras is discussed and the d-free assumption is reduced.