Abstract
Using a unitial associative ∗-algebra U over C a certain class of Hermitian finite projective modules together with a graded involutive differential algebra, both associated with U , we develop a procedure for constructing graded Lie algebras with derivation. Taking, in particular, the canonical differential algebra of Connes' theory, related to the simplest two-point K-cycle, we obtain a class of graded Lie algebras with derivation, which as one special case contains the graded Lie algebra used in the Mainz-Marseille approach to model building. Finally, we outline a new derivation of the standard model.
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