The Structures Of Lie Superalgebras Of Cartan Type

This paper mainly studies the subalgebra structures of two kinds of Lie super-algebras of Cartan type, which are Borel subalgebras of special Lie superalgebras of Cartan type and maximal root-graded subalgebras of Witt Lie superalgebras. In particular, by determining all positive root systems with respect to the canonical torus, this paper confirms all the Borel subalgebras of special Lie superalgebras of Cartan type and the connection relation between any two Borel subalgebras, and then we characterizes all the maximal root-graded subalgebras of Witt Lie superal-gebras.