# ApCoCoA-1:Coxeter Group F4

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Revision as of 15:08, 25 August 2014 by StrohmeierB (talk | contribs) (New page: === <div id="Coxeter_groups">Coxeter Group F4</div> === ==== Description ==== The F4 group is a Coxeter group. Their relations results of a Matri...)

#### Description

The F4 group is a Coxeter group. Their relations results of a Matrix, the Coxetermatrix. The Matrix with i lines and j columns gives the following relations:

<r_1,...,r_n|(r_ir_j)^m_ij

-the relation mii means: (r_ir_i)^1=1 for all i

-and other generators r_i, r_j commute.

F4 has the following presentation:

#### Reference

not found yet

#### Computation

#### Example in Symbolic Data Format

<FREEALGEBRA createdAt="2014-07-30" createdBy="strohmeier"> <vars>v,x,y,z</vars> <basis> <ncpoly>v*v-1</ncpoly> <ncpoly>x*x-1</ncpoly> <ncpoly>y*y-1</ncpoly> <ncpoly>z*z-1</ncpoly> <ncpoly>(v*x)^3-1</ncpoly> <ncpoly>(x*v)^3-1</ncpoly> <ncpoly>(v*y)^2-1</ncpoly> <ncpoly>(y*v)^2-1</ncpoly> <ncpoly>(v*z)^2-1</ncpoly> <ncpoly>(z*v)^2-1</ncpoly> <ncpoly>(x*y)^4-1</ncpoly> <ncpoly>(y*x)^4-1</ncpoly> <ncpoly>(x*z)^2-1</ncpoly> <ncpoly>(z*x)^2-1</ncpoly> <ncpoly>(y*z)^3-1</ncpoly> <ncpoly>(z*y)^3-1</ncpoly> </basis> <Comment>Coxeter_Group_F4</Comment> </FREEALGEBRA>