One way of constructing groups which are subsets of some Rn is: Let α be a finite-dimensional real algebra and let G be the group of units in α. We get more groups as subgroups of G. For example, we have used the algebra Mn(R) in which the group of units is GL(n,R) and we have the important subgroup SO(n). Our groups Spin(k) are subgroups of the group of units in the Clifford algebra Ck.
KeywordsLinear Combination Abelian Group Basis Element Unit Sphere Clifford Algebra
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