In this article, we exploit the theory of graded module categories with semi-infinite character developed by Soergel (Character formulas for tilting modules over Kac–Moody algebras, Represent. Theor. 2 (1998), 432–448) to study representations of infinite-dimensional Lie algebras of vector fields W(n), S(n) and H(n) (n \geq 2) , and obtain a description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

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In this article, we exploit the theory of graded module category with semi-infinite character developed by Soergel in [13] to study representations of the infinite dimensional Lie algebras of vector fields W (n), S(n) and H(n) (n ≥ 2), and obtain the description of indecomposable tilting modules. The character formulas for those tilting modules are determined.

The aim of this paper is to study the projective modules of the [Formula: see text]-reduced enveloping superalgebra [Formula: see text], where [Formula: see text] is the Lie superalgebra of superderivations on the Grassmann superalgebra [Formula: see text], over an algebraically closed field k of characteristic [Formula: see text]. Mainly, the Cartan invariants and the dimensions of indecomposable projective modules of [Formula: see text] are determined for any [Formula: see text]-character [Formula: see text] up to isomorphism.