definition. even subalgebra of Clifford algebra [wieser2022computing] [ca-001J]
definition. even subalgebra of Clifford algebra [wieser2022computing] [ca-001J]
The even subalgebra of the Clifford algebra is defined as the submodule of the Clifford algebra \[ \mathcal {C}\kern -2pt\ell ^{+}(Q) \equiv \left \{ x_1 \cdots x_k \in \mathcal {C}\kern -2pt\ell \mid x \in V, k \text { is even} \right \} \] which also forms a subalgebra. Its elements are called even elements, as they can be expressed as the geometric product of an even number of 1-vectors.