Integral Bases for the Universal Enveloping Algebras of Cartan Map Superalgebras

Let ?? be a finite dimensional complex simple Lie superalgebra of Cartan type and A be a commutative, associative algebra with unity over ?. We refer to the Lie superalgebras of the form ?? ? A as Cartan map superalgebras. In this paper, following Bagci and Chamberlin (J. of Pure and Applied Algebra 218(8), 1563–1576, 2014), we define an integral form for the universal enveloping algebra of the Cartan map superalgebras, and exhibit an explicit integral basis for this integral form.