Application of Clifford Algebra on Group Theory

Authors

  • Farooqhusain Inamdar Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India
  • Hasan S. N. Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India

DOI:

https://doi.org/10.37256/cm.5220243921

Keywords:

Geometric Algebra, Clifford Algebra, group action, equivalence class, principle homogeneous space, subnormal series, solvable group

Abstract

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  over the subgroup  of Clifford Algebra C(E).

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Published

2024-03-22

How to Cite

1.
Inamdar F, S. N. H. Application of Clifford Algebra on Group Theory. Contemp. Math. [Internet]. 2024 Mar. 22 [cited 2024 Jun. 17];5(2). Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3921