Automorphism groups of modular graded Lie superalgebras of Cartan-type

Abstract

Suppose the underlying field is of characteristic [Formula: see text]. In this paper, we prove that the automorphisms of the finite-dimensional graded (non-restircited) Lie superalgebras of Cartan-type [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] can uniquely extend to the ones of the infinite-dimensional Lie superalgebra of Cartan-type [Formula: see text]. Then a concrete group embedding from [Formula: see text] into [Formula: see text] is established, where [Formula: see text] is any finite-dimensional Lie superalgebra of Cartan-type [Formula: see text] or [Formula: see text] and [Formula: see text] is the underlying (associative) superalgebra of [Formula: see text]. The normal series of the automorphism groups of [Formula: see text] are also considered.