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LiE

swMATH ID: 1075
Software Authors: A.M. Cohen, B. Lisser, M.A.A. van Leeuwen
Description: LiE is the name of a software package that enables mathematicians and physicists to perform computations of a Lie group theoretic nature. It focuses on the representation theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their Weyl groups and root systems. LiE does not compute directly with elements of the Lie groups and algebras themselves; it rather computes with weights, roots, characters and similar objects. Some specialities of LiE are: tensor product decompositions, branching to subgroups, Weyl group orbits, reduced elements in Weyl groups, distinguished coset representatives and much more. These operations have been compiled into the program which results in fast execution: typically one or two orders of magnitude faster than similar programs written in a general purpose program.
The LiE programming language makes it possible to customise and extend the package with more mathematical functions. A user manual is provided containing many examples.
LiE establishes an interactive environment from which commands can be given that involve basic programming primitives and powerful built-in functions. These commands are read by an interpreter built into the package and passed to the core of the system. This core consists of programs representing some 100 mathematical functions. The interpreter offers on-line facilities which explain operations and functions, and which give background information about Lie group theoretical concepts and about currently valid definitions and values. Computer algebra system (CAS).
Homepage: http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/
Keywords: orms
Related Software: Magma; Mathematica; Macaulay2; GAP; Maple; SageMath; CHEVIE; SINGULAR; Susyno; LieART; Affine; REPSN; SARAH; Sym2Int; FORM; GitHub; OEIS; coxeter; CoReLG; ELIAS
Referenced in: 163 Publications
This software is also referenced in ORMS.
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Referenced by 227 Authors

10 Noël, Alfred G.
9 Manivel, Laurent
6 Cohen, Arjeh Marcel
6 Samtleben, Henning
5 Jackson, Steven Glenn
4 Đoković, Dragomir Ž.
4 Kleinschmidt, Axel
4 Landsberg, Joseph Montague
3 Helminck, Aloysius G.
3 Pecher, Tobias
3 Sam, Steven V.
3 Schwarz, Gerald Walter
3 Weyman, Jerzy M.
2 Abuaf, Roland
2 Avdeev, Roman S.
2 Benedetti, Vladimiro
2 Boels, Rutger H.
2 Bremner, Murray R.
2 Daniel, Jennifer Renee
2 de Graaf, Willem Adriaan
2 de Wit, Bernard
2 Dietrich, Heiko
2 Draisma, Jan
2 Faccin, Paolo
2 García-Etxebarria, Iñaki
2 Gomis, Joaquim
2 Heidenreich, Ben
2 Hentzel, Irvin Roy
2 Macfarlane, Alan J.
2 Nurowski, Paweł
2 Oeding, Luke
2 Petukhov, Alexey V.
2 Pfeiffer, Hendryk
2 Smilga, Ilia
2 Voight, John Michael
2 Wales, David B.
2 Wimmer, Robert
1 Abramson, David
1 Achar, Pramod N.
1 Aldazabal, Gerardo
1 Altunbulak, Murat
1 Assaf, Eran
1 Barthel, Tobias
1 Bates, Daniel J.
1 Bendel, Christopher P.
1 Bernig, Andreas
1 Böckle, Gebhard
1 Bödi, Richard
1 Bogdanov, Alexander V.
1 Borwein, Jonathan Michael
1 Bossard, Guillaume
1 Boulanger, Nicolas
1 Bruns, Winfried
1 Bulois, Michaël
1 Cámara, Pablo G.
1 Campo, Nobert A.
1 Can, Mehmet
1 Carr, Michael
1 Cartwright, Dustin A.
1 Chari, Vyjayanthi
1 Chirivì, Rocco
1 Conca, Aldo
1 Danila, Gentiana
1 Davis, Donald M.
1 De Loera, Jesús A.
1 De Vos, Alexis
1 Deligne, Pierre René
1 Derksen, Harm
1 Diamond, Benjamin E.
1 Dongarra, Jack J.
1 Erdmenger, Johanna
1 Erman, Daniel
1 Evtikhiev, Mikhail
1 Faenzi, Daniele
1 Feger, Robert
1 Fernández-Núñez, José
1 Figueroa-O’Farrill, José Miguel
1 Filippini, Sara Angela
1 Fretwell, Dan
1 Fuchssteiner, Benno
1 Galaev, Anton S.
1 García Fuertes, Wilfredo
1 Garibaldi, Skip
1 Gates, Sylvester James jun.
1 Gerdt, Vladimir Petrovich
1 Gervais, Jean-Loup
1 Godliński, Michał
1 Gorbachev, Yuriy E.
1 Grabowski, Jan Edward
1 Greenberg, Matthew
1 Greenstein, Jacob
1 Griess, Robert L. jun.
1 Gross, Benedict Hyman
1 Gruson, Laurent
1 Gui, Bin
1 Güner, Rıdvan
1 Hague, Chuck
1 Halawi, Hezi
1 Henderson, Anthony
1 Herbig, Hans-Christian
...and 127 more Authors
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Referenced in 67 Serials

16 Journal of High Energy Physics
8 Journal of Algebra
8 Transformation Groups
6 Advances in Mathematics
5 Journal of Geometry and Physics
5 Journal of Symbolic Computation
5 Experimental Mathematics
4 Communications in Mathematical Physics
4 Nuclear Physics. B
4 Annales de l’Institut Fourier
4 Journal of Pure and Applied Algebra
4 Algebras and Representation Theory
3 Communications in Algebra
3 Representation Theory
2 Classical and Quantum Gravity
2 Computer Physics Communications
2 Journal of Mathematical Physics
2 Mathematics of Computation
2 Compositio Mathematica
2 Journal of Functional Analysis
2 Mathematische Zeitschrift
2 Annals of Physics
2 Journal of Algebraic Combinatorics
2 Journal of Lie Theory
2 Selecta Mathematica. New Series
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 International Journal of Modern Physics A
1 Israel Journal of Mathematics
1 Duke Mathematical Journal
1 Inventiones Mathematicae
1 Journal of the London Mathematical Society. Second Series
1 Journal of Mathematics of Kyoto University
1 Manuscripta Mathematica
1 Memoirs of the American Mathematical Society
1 Michigan Mathematical Journal
1 Numerische Mathematik
1 Proceedings of the American Mathematical Society
1 Proceedings of the London Mathematical Society. Third Series
1 Programming and Computer Software
1 Discrete & Computational Geometry
1 Mathematical and Computer Modelling
1 CWI Quarterly
1 International Journal of Mathematics
1 IMRN. International Mathematics Research Notices
1 Seminar Sophus Lie
1 Journal of Physics A: Mathematical and General
1 Linear Algebra and its Applications
1 SIAM Review
1 Expositiones Mathematicae
1 Euromath Bulletin
1 Communications in Analysis and Geometry
1 Journal of Mathematical Sciences (New York)
1 The Electronic Journal of Combinatorics
1 Vietnam Journal of Mathematics
1 Geometry & Topology
1 Mathematical & Computational Applications
1 Qualitative Theory of Dynamical Systems
1 Foundations of Computational Mathematics
1 Central European Journal of Mathematics
1 Hacettepe Journal of Mathematics and Statistics
1 Journal of Algebra and its Applications
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
1 Oberwolfach Reports
1 Encyclopaedia of Mathematical Sciences
1 Lecture Notes in Computer Science
1 Research in Number Theory
1 Springer Undergraduate Texts in Mathematics and Technology

Referencing Publications by Year