  Division algebras have demonstrated their utility in studying non-associative
algebras and their connection to the Standard Model through complex Clifford
algebras. This article focuses on exploring the connection between these
complex Clifford algebras and their corresponding real Clifford algebras
providing insight into geometric properties of bivector gauge symmetries. We
first generate gauge symmetries in the complex Clifford algebra through a
general Witt decomposition. Gauge symmetries act as a constraint on the
underlying real Clifford algebra, where they're then translated from their
complex form to their bivector counterpart. Spin group arguments allow the
identification of bivector structures which preserve the gauge symmetry
yielding the corresponding real Clifford algebra. We conclude that Standard
Model gauge groups emerge from higher-dimensional Clifford algebras carrying
Euclidean signatures, where particle states are recognized as a combination of
basis elements corresponding to complex Euclidean Clifford algebras.
