It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie
group can be represented as a spin group. Thus, the computational power of geometric
algebra is available to simplify the analysis and applications of Lie groups and Lie algebras.
The spin version of the general linear group is thoroughly analyzed, and an invariant
method for constructing real spin representations of other classical groups is developed.
Moreover, it is demonstrated that every linear transformation can be represented as a …