Exceptional $\mathfrak{g}_2$ deformations and gauge symmetries

Deformed $\mathfrak{g}_2$ exceptional applications are introduced via the Clifford algebra-parametrized formalism. Using the products between multivectors of $\cl_{0,7}$, the Clifford algebra over the metric vector space $\RR^{0,7}$, and octonions, resulting in an octonion, we generalize the exceptional Lie algebra $\mathfrak{g}_2$ applications, also associated with the transformation rules for bosonic and fermionic fields on the 7-sphere $S^7$. The emergence of $SU(3)$-like subalgebras within the exceptional Lie algebra $\mathfrak{g}_2$ provides an algebraic framework reminiscent of the $SU(3)$ gauge symmetry of QCD.

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