Maximal Graded Subalgebras And Derivation Algebras Of The General Linear Lie Superalgebra Over Superrings

In this paper, we determine all maximal graded subalgebras of the general linear Lie superalgebras containing the standard Cartan subalgebra over a unital supercommutative superring with 2 invertible. Secondly, we conceretely described the Z-derivations of the general linear Lie superalgebras over a unital commutative ring with 2 invertible through the method of calculating the effect of the derivations on basic elements.