CANONIK swMATH ID: 12229 Software Authors: Rand, D.W. Description: PASCAL programs for identification of Lie algebras. III: Levi decomposition and canonical basis. These are the last parts of a program package based on PASCAL for the identification of a Lie algebra L (given by its structure constants) by computer means. The program LEVI (5100 lines) calculates by a recursive algorithm the semisimple part S(L), of L, together with the radical R(L) (determined by RADICAL, a program presented earlier) there is then realized a Levi decomposition of L. The program CANONIK (10300 lines) uses the parts RADICAL, SPLIT (also presented earlier) and LEVI to present a given Lie algebra with a standardized basis and gives possibilities for its comparison with other Lie algebras. Examples of Lie algebras with canonical bases of dim=10 are given, for the theory of applied algorithms see also Zbl 0668.17004. With respect to the examples and informations the whole package presented by the authors seems to be very effective and useful. Homepage: http://www.cpc.cs.qub.ac.uk/summaries/AAXO_v1_0.html Keywords: canonical basis; computer algebra; program package; Lie algebra; recursive algorithm; Levi decomposition Related Software: SPLIT; SYMMGRP.MAX; diffgrob2; ELIAS; Maple; Galaxy; pLoc-mEuk; iACP; iSS-PseDNC; GRAPH; ifs; CHomP; FlowLab; SPOT; ROptEst; DISCRETA; libagf; ELECTRE; SaddleDrop; R Cited in: 24 Documents all top 5 Cited by 28 Authors 6 Winternitz, Pavel 5 de Graaf, Willem Adriaan 2 Ivanyos, Gábor 2 Reid, Gregory John 2 Rónyai, Lajos 2 Šnobl, Libor 1 Agaoka, Yoshio 1 Ait Abdelmalek, M. 1 Boulton, Alan 1 Bracken, Paul Francis 1 Clarkson, Peter A. 1 Fisher, David J. 1 Gray, Robert J. 1 Grundland, Alfred Michel 1 Hrivnák, Jiří 1 Hydon, Peter Ellsworth 1 Kanatchikov, Igor V. 1 Küronya, Alex 1 Leng, Xiaodan 1 Lisle, Ian G. 1 MacCallum, Malcolm A. H. 1 Ndogmo, Jean-Claude 1 Nikolaevskiĭ, Yuriĭ A. 1 Novotný, Petr 1 Patera, Jiří 1 Rand, D. W. 1 Schwarz, Fritz 1 Wittkopf, Allan D. all top 5 Cited in 12 Serials 3 Journal of Physics A: Mathematical and General 2 Linear Algebra and its Applications 2 Applicable Algebra in Engineering, Communication and Computing 2 Journal of Physics A: Mathematical and Theoretical 1 Computer Physics Communications 1 Journal of Mathematical Physics 1 Reports on Mathematical Physics 1 Journal of Pure and Applied Algebra 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 European Journal of Applied Mathematics 1 Pure and Applied Mathematics (Boca Raton) all top 5 Cited in 11 Fields 17 Nonassociative rings and algebras (17-XX) 9 Partial differential equations (35-XX) 7 Computer science (68-XX) 3 Topological groups, Lie groups (22-XX) 3 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 1 Associative rings and algebras (16-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) Citations by Year