LieART swMATH ID: 8573 Software Authors: Robert Feger, Thomas W. Kephart Description: LieART - A Mathematica Application for Lie Algebras and Representation Theory. We present the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART’s user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix. Homepage: http://lieart.hepforge.org/ Dependencies: Mathematica Related Software: Mathematica; Susyno; LiE; Affine; GAP; Adinkras; GitHub; Sym2Int; PyR@TE; SARAH; GroupMath; DLMF; adynkra; Keras; SageMath; HEPTHools; JuliBootS; PyCFTBoot; CBoot; SDPB Cited in: 58 Publications all top 5 Cited by 105 Authors 6 Nepomechie, Rafael I. 4 Retore, Ana L. 3 Hu, Yangrui 3 Kim, Sung-Soo 3 Mak, S.-N. Hazel 2 Apruzzi, Fabio 2 Danielsson, Ulf H. 2 Dibitetto, Giuseppe 2 Gates, Sylvester James jun. 2 Hanany, Amihay 2 Hayashi, Hirotaka 2 Heckman, Jonathan J. 2 Isaev, Alekseĭ Petrovich 2 Kalveks, Rudolph 2 Kephart, Thomas W. 2 Kim, Hee-Cheol 2 Kim, Joonho 2 Lee, Kimyeong M. 2 Mitev, Vladimir 2 Ohmori, Kantaro 2 Pimenta, Rodrigo A. 2 Yagi, Futoshi 1 Abzalov, Aidar 1 Agarwal, Prarit 1 Avetisyan, M. Y. 1 Bakhmatov, Ilya 1 Benli, Seçil 1 Biggio, Carla 1 Bordone, Marzia 1 Braun, Andreas P. 1 Chacaltana, Oscar 1 Chen, Heng-Yu 1 Chen, Jin 1 Córdova, Clay 1 Cvetič, Mirjam 1 de Medeiros, Paul 1 Dereli, Tekin 1 Di Luzio, Luca 1 Distler, Jacques 1 Dumitrescu, Thomas T. 1 Dupuis, Éric 1 Fazzi, Marco 1 Feger, Robert 1 Fendley, Paul 1 Fonseca, Renato M. 1 Grau, Aleix Gimenez 1 Hadasz, Leszek 1 Haghighat, Babak 1 Hahn, Heekyoung 1 Hasebe, Kazuki 1 Haßler, Falk 1 He, Yang-Hui Evariste 1 Hollands, Lotte 1 Hollands, Stefan 1 Hwang, Chiung 1 Intriligator, Kenneth 1 James Gates, S. jun. 1 Kashani-Poor, Amir-Kian 1 Kim, Seok 1 Kristjansen, Charlotte F. 1 Krivonos, S. O. 1 Lal, Shailesh 1 Lee, Ki-Hong 1 Liendo, Pedro 1 Lin, Ling 1 Lysenko, Sergey 1 Majumder, Suvajit 1 Martucci, Luca 1 Matassa, Marco 1 Meneghelli, Carlo 1 Mkrtchyan, Ruben L. 1 Moriyama, Sanefumi 1 Mukhi, Sunil 1 Muralidhara, Girish 1 Musaev, Edvard T. 1 Neitzke, Andrew 1 Nibbelin, Stefan Groot 1 Nii, Keita 1 Nosaka, Tomoki 1 Oehlmann, Paul-Konstantin 1 Park, Jaemo 1 Pilch, Krzysztof 1 Pomoni, Elli 1 Provorov, A. A. 1 Raghuram, Nikhil 1 Ridolfi, Giovanni 1 Rochais, Thomas B. 1 Ruba, Błażej 1 Rudolph, Gerd 1 Ruehle, Fabian 1 Schmidt, Matthias 1 Sheridan, Elijah 1 Song, Jaewon 1 Sperling, Marcus 1 Taki, Masato 1 Taylor, Washington IV 1 Trimm, Anderson 1 Volk, Matthias 1 Wang, Chunguang 1 Warner, Nicholas P. ...and 5 more Authors all top 5 Cited in 14 Serials 34 Journal of High Energy Physics 6 Nuclear Physics. B 4 Journal of Mathematical Physics 3 Communications in Mathematical Physics 2 Journal of Physics A: Mathematical and Theoretical 1 Classical and Quantum Gravity 1 Computer Physics Communications 1 International Journal of Theoretical Physics 1 Journal of Statistical Physics 1 Physics Letters. B 1 Theoretical and Mathematical Physics 1 Proceedings of the American Mathematical Society 1 Geometric and Functional Analysis. GAFA 1 Annals of Physics all top 5 Cited in 24 Fields 48 Quantum theory (81-XX) 24 Relativity and gravitational theory (83-XX) 12 Nonassociative rings and algebras (17-XX) 7 Algebraic geometry (14-XX) 7 Statistical mechanics, structure of matter (82-XX) 3 Topological groups, Lie groups (22-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 2 Number theory (11-XX) 2 Associative rings and algebras (16-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Functional analysis (46-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) Citations by Year