Isomorphism groups in Clifford algebras (Q1975593)

The author defines in a Clifford algebra an orthonormal basis (ONB) set of multivectors. Further, products of such multivectors are considered and represented as row matrices. It is verified that between the Clifford algebra \(Cl_{p,q}\) and \(Cl'\), the algebra generated by all vectors, exists an isomorphism. In the four-dimensional case ONBs are computed by computer algebra calculations. There is lined out that the main automorphism and antiautomorphism in a Clifford algebra essentially depend on the chosen basis. Possible applications of such multivector transformations should be searched in physics.