Abstract: In the sense of generalized restricted Lie algebras, it was proved that the modified induced modules of graded Lie algebras of Cartan types W, S, H coincide with coinduced modules. The relationship between induced modules and coinduced modules was obtained, extending the corresponding result by Rolf Farnsteiner and Helmut Strade in the case of restricted Lie algebras. Therefore, it was proved that any irreducible non-exceptional modules for graded Lie algebras of Cartan types W, S, H with generalized p-character of height not more than a precise upper-bound is a coinduced module. By applying this with some results on cohomology obtained by Rolf Farnsteiner in 1990s, we finally got some further results on extensions between simple modules of graded Lie algebras of Cartan types W, S, H.

Key words: Cartan type Lie algebra, induced module, coinduced module, extension, generalized restricted Lie algebra, Cartan type Lie algebra, induced module, coinduced module, extension