Application of Clifford Algebra on Group Theory
DOI:
https://doi.org/10.37256/cm.5220243921Keywords:
Geometric Algebra, Clifford Algebra, group action, equivalence class, principle homogeneous space, subnormal series, solvable groupAbstract
The orthogonal operators defined as similarity transformations on Euclidean space E can also be considered as group actions on the Clifford Algebra. In this paper, we investigate the finite subgroup of Euclidian space E of Geometric Algebra over a finite dimension vector space E. The hierarchy of the finite subgroups of Clifford Algebra C(E) is depicted through the lattice structure and we discussed the group action of these subgroups on the vector space E. Further, we shall address the number of non-trivial finite subgroups, Normal subgroups, and subnormal series of the subgroup of Clifford Algebra C(E) constructed over the vector space E by performing group action Ψ: B3 × B3 → B3 over the subgroup B3 of Clifford Algebra C(E).
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Copyright (c) 2024 Farooqhusain Inamdar, et al.
This work is licensed under a Creative Commons Attribution 4.0 International License.