Field theory equations with spinor gauge symmetry

On generalization of Lipschitz groups and spin groups

“…Study of the corresponding Lie groups in degenerate geometric algebras $$$ {\mathcal{G}}_{p,q,r} $$$, which are widely used in different applications, is another interesting problem for further research. Being the generalizations of the standard Lipschitz and spin groups, the groups introduced in this paper may be useful for various applications in physics, 1,21–24 engineering, 25–28 computer science 26,27,29–31 (in particular, for neural networks 32 and image processing 33 ), and other sciences.…”

“…Since the reversion changes the sign of the element TUT −1 , we have TUT −1 ∈  23 for any U ∈  23 . Thus, T ∈ Γ23 .…”

“…The groups Pin A + and Pin B + are considered in previous works, [16][17][18] where they are denoted by G 23 and G 12 in the real case F = R and G 23i23 and G 12i12 in the complex case F = C, respectively. In these three papers, isomorphisms between Pin A + , Pin B + , and classical matrix Lie groups are proved in the case of arbitrary dimension and signature.…”