General Mathematics

    

Deformed Lie Products and Involution - Second Part: in a Four-dimensional Space.

Authors: Thierry L.A. Periat

A previous document laid the foundations for the study of involution in any three-dimensional spaces, [c]. This exploration continues the exploration of the topic in focusing now attention on four-dimensional spaces. The repetition of a deformed Lie product on a given argument carries two concepts with it: (i) the eventual invariance of this argument and (ii) the existence of an involution. The work discovers two distinct classes of decomposition without residual part for each deformed Lie product. It explains why only one of both (the simplest one) can characterize the involution when the deforming cube is anti-symmetric and anti-reduced. The document also starts a confrontation between the simplest representation and the electromagnetic duality in Maxwell's vacuum.

Comments: 40 Pages.

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[v1] 2025-07-08 12:45:51

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