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LieRing

Computing with finitely presented Lie rings

Version 2.4.2

10 February 2022

Serena Cicalò
Email: cicalo@science.unitn.it
Address:
Serena Cicalò
Dipartimento di Matematica e Informatica
Via Ospedale 72
Italy

Willem Adriaan de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf

Abstract

This package provides functions for constructing and working with Lie rings. There are functions for dealing with finitely-presented Lie rings, and for performing the Lazard correspondence. The package also contains a small database of finitely-generated Lie rings satisfying an Engel condition.

Copyright

© 2016 Serena Cicalò and Willem de Graaf

Contents

1 Introduction
 1.1 Preliminaries
 1.2 The free Lie ring
 1.3 The Lazard correspondence
2 The functions
 2.1 The free Lie ring

  2.1-1 FreeLieRing
  2.1-2 Degree
 2.2 Creating Lie rings

  2.2-1 IsLieRing
  2.2-2 LieRingByStructureConstants
  2.2-3 FpLieRing
  2.2-4 FpLieAlgebra
 2.3 Working with Lie rings

  2.3-1 Basis
  2.3-2 StructureConstantsTable
  2.3-3 Torsion
  2.3-4 Coefficients
  2.3-5 SubLieRing
  2.3-6 LieRingIdeal
  2.3-7 NaturalHomomorphismByIdeal
  2.3-8 LieLowerCentralSeries
  2.3-9 LieLowerPCentralSeries
  2.3-10 LieCentre
  2.3-11 TensorWithField
 2.4 The Lazard correspondence

  2.4-1 PGroupToLieRing
  2.4-2 LieRingToPGroup
 2.5 The database of \(n\)-Engel Lie rings

  2.5-1 SmallNEngelLieRing
References
Index

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