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The aim of this paper is to study some properties of the algebra of absolute invariant operators which produce trace decomposition of tensors. The emphasis is on the family of projections, which do provide insight of some problems of differential geometry, getting a decomposition of the space of tensors of type (1, 3) into three components, invariant under the group GL(V), in infinitely many possibilities, generalizing in this way the Strichartz splitting of curvature tensors. The extension offatcat:sqzj44jk5nfxvgndsikwjbn3ae