Dr. Erik Trell

Abstract:

The original Lie linear algebra [1-3] is the only true linear algebra since it is the line that is the building element, a real “Ding” [1] that does the job in the constructions it puts together bit by bit, step by step, ”as a partial differential equation itself” in the “form f( x y z dx dy dz) = 0” [2,3]. Both the xyz coordinate axes (at the limit scale behaving like quarks) and the dx dy dz partial derivatives are “straight lines of length equal to zero” [Ib.] and thus the infinitesimal generators of what they singly or in constellations outline in a sequential crystallization of “Figuren” [1] in one “Nullstreifen” [Ib.], two “algebraische Fläche” [Ib.] or three - conforming with Schrödinger wavepackets -  “complex-cone” [2-3] dimensions to, for instance, “in that we restrict ourselves to the linear transformations of r, we find between the corresponding transformations of R: all movements (translation movement, rotation-movement, and the helicoidal movement), semblability transformations, transformation by reciprocal radii, parallel transformation…etc”. [Ib.] Each of these is a Lie group  shaped by the algebra  over a range corresponding e.g. to infinitely small displacements about some angle θ,  and since what is presently called Lie algebra  was obtained by deriving such ‘infinitesimal actions’ from the group the baby initially lost by lack of translation is now lost in translation, too, to an analog tail-of-the-dog resultant “linear vector space” whose however majestic coordinate matrices and renormalization factors  never lead back to the original infinitesimal generator “curve net” [2,3] in which the Standard Model can exactly and exhaustively be tracked down by serial interior volume-preserving lattice transformations [4], and the Periodic System equally exactly and exhaustively by its exterior space-filling modular Aufbau [5-8], all of which at the same time providing accurate images and models as well as online interactive computer program bits and algorithms [6-8].