### 7.10.2 fpalgebras_lib

Library:
  fpalgebras.lib
Purpose:
  Definitions of some finitely presented algebras and groups (Letterplace)
Authors:
  Karim Abou Zeid, karim.abou.zeid at rwth-aachen.de
  Viktor Levandovskyy, viktor.levandovskyy at math.rwth-aachen.de
  Grischa Studzinski, grischa.studzinski at rwth-aachen.de

  Support: Project II.6 in the transregional collaborative research centre SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German DFG

Overview:
  Generation of various algebras, including group algebras of finitely presented groups in the Letterplace ring. FPA stands for finitely presented algebra.

Procedures:

> 7.10.2.1 operatorAlgebra |  | description of some common algebras of operators
> 7.10.2.2 serreRelations |  | compute the homogeneous part of Serre's relations associated to a generalized Cartan matrix A
> 7.10.2.3 fullSerreRelations |  | compute the ideal of all Serre's relations associated to a generalized Cartan matrix A
> 7.10.2.4 ademRelations |  | compute the ideal of Adem relations for i<2j in char 0
> 7.10.2.5 baumslagSolitar |  |
> 7.10.2.6 baumslagGroup |  |
> 7.10.2.7 crystallographicGroupP1 |  |
> 7.10.2.8 crystallographicGroupPM |  |
> 7.10.2.9 crystallographicGroupPG |  |
> 7.10.2.10 crystallographicGroupP2MM |  |
> 7.10.2.11 crystallographicGroupP2 |  |
> 7.10.2.12 crystallographicGroupP2GG |  |
> 7.10.2.13 crystallographicGroupCM |  |
> 7.10.2.14 crystallographicGroupC2MM |  |
> 7.10.2.15 crystallographicGroupP4 |  |
> 7.10.2.16 crystallographicGroupP4MM |  |
> 7.10.2.17 crystallographicGroupP4GM |  |
> 7.10.2.18 crystallographicGroupP3 |  |
> 7.10.2.19 crystallographicGroupP31M |  |
> 7.10.2.20 crystallographicGroupP3M1 |  |
> 7.10.2.21 crystallographicGroupP6 |  |
> 7.10.2.22 crystallographicGroupP6MM |  |
> 7.10.2.23 dyckGroup1 |  |
> 7.10.2.24 dyckGroup2 |  |
> 7.10.2.25 dyckGroup3 |  |
> 7.10.2.26 fibonacciGroup |  |
> 7.10.2.27 tetrahedronGroup |  |
> 7.10.2.28 triangularGroup |  |

See also: LETTERPLACE; fpadim_lib; fpaprops_lib; freegb_lib.

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