Finite group graded Lie algebraic extensions and trefoil symmetric relativity, standard model, Yang Mills and gravity theories

We introduce the Quotient Group Graded Lie algebras, which involve graded structure constants. This structure is then used to obtain a graded extension of supersymmetry where diverse features of the Standard Model of elementary particles arise naturally. For the Minimal Vector Clover Extension of the symmetries of special relativity, we develop the extended superspace formalism in differential geometric language. We construct connections, curvature, and prove Bianchi identities both in coordinate and in symmetry covariant bases. We study also a connection making the Lorentz symmetry point dependent, its torsion and curvature. Moreover, we examine a transformation that removes noncommutativity from the Minimal Vector Clover Extension.