TY - JOUR
AU - Inamdar, Farooqhusain
AU - S. N., Hasan
PY - 2024/03/22
Y2 - 2024/05/31
TI - Application of Clifford Algebra on Group Theory
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 5
IS - 2
SE - Research Article
DO - 10.37256/cm.5220243921
UR - https://ojs.wiserpub.com/index.php/CM/article/view/3921
SP -
AB - <p>The orthogonal operators defined as similarity transformations on Euclidean space <em>E</em> can also be considered as group actions on the Clifford Algebra. In this paper, we investigate the finite subgroup of Euclidian space <em>E</em> of Geometric Algebra over a finite dimension vector space <em>E</em>. The hierarchy of the finite subgroups of Clifford Algebra <em>C(E)</em> is depicted through the lattice structure and we discussed the group action of these subgroups on the vector space<em> E</em>. Further, we shall address the number of non-trivial finite subgroups, Normal subgroups, and subnormal series of the subgroup of Clifford Algebra <em>C(E)</em> constructed over the vector space <em>E</em> by performing group action over the subgroup of Clifford Algebra <em>C(E).</em></p>
ER -