Difference between revisions of "ApCoCoA-1:Coxeter groups"

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The Matrix with i lines and j columns gives the following relations:
 
The Matrix with i lines and j columns gives the following relations:
  
  <r1,...,rn|(rirj)^mij
+
  <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.
 +
 
 +
H3 has the following presentation:
  
 
==== Reference ====
 
==== Reference ====

Revision as of 18:54, 24 August 2014

Description

The full icosahedral 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.

H3 has the following presentation:

Reference

not found yet

Computation

Example in Symbolic Data Format

<FREEALGEBRA createdAt="2014-07-30" createdBy="strohmeier">
	<vars>x,y,z</vars>
	<basis>
	<ncpoly>x*x-1</ncpoly>
	<ncpoly>y*y-1</ncpoly>
	<ncpoly>z*z-1</ncpoly>
	<ncpoly>(x*y)^5-1</ncpoly>
	<ncpoly>(y*x)^5-1</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_H3</Comment>
</FREEALGEBRA>