Block degeneracy and Cartan invariants for graded Lie algebras of Cartan type (Q1320254)

The authors first show that the restricted Lie algebras of Cartan type are of one block type, i.e., the restricted universal enveloping algebra of such a Lie algebra \(L\) has only one block. The remaining part of the article is dedicated to the investigation of the Cartan invariants \(c_{\lambda,\mu}\) of \(L\). It is shown that the computation of \(c_{\lambda,\mu}\) can be reduced to the computation of the Cartan invariants of the zero grade term \(L_ 0\) which is classical. In particular, the Cartan matrix \(C= (c_{\lambda,\mu})\) is computed explicitly for \(L= H(2,\underline 1)\).