[1X[5XLieAlgDB[0m[1X[0m [1XA database of Lie algebras[0m Version 2.0.2 September 2007 Willem de Graaf Csaba Schneider Willem de Graaf Email: [7Xmailto:degraaf@science.unitn.it[0m Homepage: [7Xhttp://www.science.unitn.it/~degraaf/[0m Address: Dipartimento di Matematica Via Sommarive 14 I-38050 Povo (Trento) Italy Csaba Schneider Email: [7Xmailto:csaba.schneider@sztaki.hu[0m Homepage: [7Xhttp://www.sztaki.hu/~schneider[0m Address: Informatics Research Laboratory Computer and Automation Research Institute 1518 Budapest Pf. 63. Hungary ------------------------------------------------------- [1XAbstract[0m This package provides access to the classification of the following families of Lie algebras: -- non-solvable Lie algebras over finite fields up to dimension 6; -- nilpotent Lie algebras of dimension up to 9 over [3XGF(2)[0m, of dimension up to 7 over [3XGF(3)[0m or [3XGF(5)[0m; -- simple Lie algebras of dimensions between 7 and 9 over [3XGF(2)[0m; -- the classification of solvable Lie algebras of dimension at most 4; -- the classification of nilpotent Lie algebras of dimensions at most 5 and those of dimension 6 over fields of odd characteristic. ------------------------------------------------------- [1XCopyright[0m © 2006--2007 Willem de Graaf and Csaba Schneider ------------------------------------------------------- [1XAcknowledgements[0m We are grateful to Andrea Caranti, Marco Costantini, Bettina Eick, Helmut Strade, Michael Vaughan-Lee. Without their help, interest, and encouragement, this package would not have been completed. We also acknowledge the effort of the referees to improve the implementation and the documentation. ------------------------------------------------------- [1XContents (LieAlgDB)[0X 1 Introduction 2 The families of Lie algebras included in the database 2.1 Non-solvable Lie algebras 2.1-1 NonSolvableLieAlgebra 2.1-2 Dimension 1 and 2 2.1-3 Dimension 3 2.1-4 Dimension 4 2.1-5 Dimension 5 2.1-6 Dimension 6 2.1-7 AllNonSolvableLieAlgebras 2.1-8 AllSimpleLieAlgebras 2.2 Solvable and nilpotent Lie algebras 2.2-1 SolvableLieAlgebra 2.2-2 NilpotentLieAlgebra 2.2-3 AllSolvableLieAlgebras 2.2-4 AllNilpotentLieAlgebras 2.2-5 NumberOfNilpotentLieAlgebras 2.2-6 LieAlgebraIdentification 3 A description of the Lie algebras that are contained in the package 3.1 Description of the non-solvable Lie algebras 3.2 Dimension 3 3.3 Dimension 4 3.4 Dimension 5 3.4-1 Characteristic 2 3.4-2 Odd characteristic 3.5 Dimension 6 3.5-1 Characteristic 2 3.5-2 General odd characteristic 3.5-3 Characteristic 3 3.5-4 Characteristic 5 3.6 Description of the simple Lie algebras 3.7 Description of the solvable and nilpotent Lie algebras -------------------------------------------------------