Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)

Mehmet Koca; Mudhahir Al-Ajmi; Nazife Ozdes Koca

doi:10.1142/S0219887813500102

Quaternionic construction of the W(F₄) polytopes with their dual polytopes and branching under the subgroups W(B₄) and W(B ₃) × W(A₁)

Mehmet Koca^*, Mudhahir Al-Ajmi, Nazife Ozdes Koca

^*Corresponding author for this work

Physics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Four-dimensional F₄ polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F₄ ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F₄ ) orbit under the Coxeter groups W(B₄) and W(B₃) × W(A₁) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

Original language	English
Article number	1350010
Journal	International Journal of Geometric Methods in Modern Physics
Volume	10
Issue number	5
DOIs	https://doi.org/10.1142/S0219887813500102
Publication status	Published - May 2013

Keywords

4D polytopes
Coxeter groups
W(F)
dual polytopes
quaternions

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887813500102

Cite this

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title = "Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)",

abstract = "Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.",

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T1 - Quaternionic construction of the W(F4) polytopes with their dual polytopes and branching under the subgroups W(B4) and W(B 3) × W(A1)

AU - Koca, Mehmet

AU - Al-Ajmi, Mudhahir

AU - Koca, Nazife Ozdes

PY - 2013/5

Y1 - 2013/5

N2 - Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

AB - Four-dimensional F4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(F4 ) where the group elements and the vertices of the polytopes are represented by quaternions. Branchings of an arbitrary W(F4 ) orbit under the Coxeter groups W(B4) and W(B3) × W(A1) have been presented. The role of group theoretical technique and the use of quaternions have been emphasized.

KW - 4D polytopes

KW - Coxeter groups

KW - W(F)

KW - dual polytopes

KW - quaternions

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