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# LieRing

## Lie Rings

Version 2.3

November 2016

Serena Cicalò
Email: cicalo@science.unitn.it
Address:
Dipartimento di Matematica e Informatica
Via Ospedale, 72
09124 Cagliari
Italy

Willem de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf/
Address:
Dipartimento di Matematica
Via Sommarive 14
I-38050 Povo (Trento)
Italy

### 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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