Lie Theory



Reports, Theses




My Notes



V. K. Agrawala and Johan G. Belinfante; Weight diagrams for Lie group representations: A computer implementation of Freudenthal's algorithm in ALGOL and FORTRAN, BIT (1969) 9(4):301-314, doi: 10.1007/BF01935862

John C. Baez; The octonions, Bull. Amer. Math. Soc. (2002), 39:145-205, doi: 10.1090/S0273-0979-01-00934-X

Arjeh M. Cohen and Willem A. de Graaf; Lie algebraic computation, Com. Phys. Comm (1996) 97:53-62, doi: 10.1016/0010-4655(96)00021-5

Arjeh M. Cohen et al.; Computing in groups of Lie type, Math. Comp. (2004) 73:1477-1498, doi: 10.1090/S0025-5718-03-01582-5

E. de Sousa Bernardes; Killing - An algebraic computational package for Lie algebras, Computer Physics Communications (2000) 130(1-2):137-175, doi: 10.1016/S0010-4655(00)00006-0

Peter B. Gilkey; Some representations of exceptional Lie algebras, Geometricae Dedicata (1988) 25(1-3):407-416, doi: 10.1007/BF00191935

V. M. Gordienko; Matrix entries of real representations of the group O(3) and SO(3), Siberian Mathematical Journal (2002), 43(1):36-46, doi: 10.1023/A:1013816403253

Roger Howe; Very Basic Lie Theory, The American Mathematical Monthly (1983), 90(9):600-623 Correction in: (1984) 91:247

R. B. Howlett, L. J. Rylands and D. E. Taylor; Matrix generators for exceptional groups of Lie type, J. Symbolic Computation (2001) 31(4):429-445, doi: 10.1006/jsco.2000.0431

G. Itzkowitz, S. Rothman and H. Strassberg; A note on the real representation of SU(2,C), Journal of Pure and Applied Algebra (1991), 69(3):285-294, doi: 10.1016/0022-4049(91)90023-U

D. Rand, P. Winternitz and H. Zassenhaus; On the identification of a Lie algebra given by its structure constants. I. Direct decompositions, Levi decompositions, and nilradicals, Linear Algebra and its Applications (1988), 109:197-246, doi: 10.1016/0024-3795(88)90210-8

L. J. Rylands and D.E. Taylor; Matrix generators for the orthogonal groups, J. Symbolic Computation (1998) 25(3):351-360, doi: 10.1006/jsco.1997.0180

Aaron Wangberg and Tevian Dray; Visualizing Lie subalgebras using root and weight diagrams, Loci (February 2009), doi: 10.4169/loci003287


Johan G. F. Belinfante, Bernard Kolman; A survey of Lie groups and Lie algebras with applications and computational methods, SIAM, 1989, ISBN-0898712432

Manfred Böhm; Lie-Gruppen und Lie-Algebren in der Physik: Eine Einführung in die Mathematischen Grundlagen, Springer, 2011, ISBN-3642203787

Robert N. Cahn; Semi-simple Lie algebras and their representations, Dover, 2006, ISBN-0486449998

Roger W. Carter; Simple groups of Lie type, Wiley, 1972, ISBN-0471137359

Nathan C. Carter; Visual group theory, The Mathematical Association of America, 2009, ISBN-088385757X

Marvin Chester; Primer of quantum mechanics, Dover, 2003, ISBN-0486428788

J. P. Elliott, P. G. Dawber; Symmetry in physics, Volume 1: Principles and simple applications Volume 2: Further applications, Macmillan, 1979, ISBN-0333382722

Willem A. de Graaf; Lie algebras: Theory and Applications, North-Holland, 2000, ISBN-0444501169

Jürgen Fuchs, Christoph Schweigert; Symmetries, Lie algebras and representations Cambridge University Press, 1994, ISBN-0521560012

Howard Georgi; Lie algebras in particle physics, Westview Press, 1999, ISBN-0738202339

Robert Gilmore; Lie groups, physics and geometry, Cambridge University Press, 2008, ISBN-9780521884006

Willem A. De Graaf; Lie algebras, Theory and algorithms, North Holland, 2000, ISBN-0444501169

James E. Humphreys; Introduction to Lie algebras and representation theory, Springer, 1973, ISBN-0387900535

Nathan Jacobson; Lie algebras, Courier Dover Publications, 1979, ISBN-0486638324

Hugh F. Jones; Group theory and physics, IOP Publishing, 1990, ISBN-0852740301

Harry J. Lipkin; Lie Groups for Pedestrians, Courier Dover Publications, 2002, ISBN-0486421856

R. Mirmin; Group theory: An intuitive approach, World Scientific, 1995, ISBN-9810233655

Shlomo Sternberg; Group theory and physics, Cambridge University Press, 1994, ISBN-0521558859

John Stillwell; Naive Lie theory, Springer, 2008, ISBN-9780387782140

Kristopher Tapp; Matrix groups for undergraduates, American Mathematical Society, 2005, ISBN-0821837850

V. S. Varadarajan; Lie groups, Lie algebras and their representations, Springer, 1984, ISBN-0387909699

Brian G. Wybourne; Classical Groups for physicists, Wiley, 1974, ISBN-0471965057

Reports, Theses

R. J. Riebeek; Computations in Association Schemes, PhD dissertation (1998), Technical University Eindhoven, Netherlands, available online (accessed June 2014)


Home page of Prof. John Baez at UC Riverside (see, e.g., this page)

Atlas of Lie groups and representations


LieTools are a set of MATLAB tools attempting to visualize structure constants of classical and exceptional Lie algebras.


My semi-simple-minded thoughts on the visualization of Lie theory concepts

My Notes

Title: A note on random samples of Lie algebras (arXiv:1407.3642)
Abstract: Recently, Paiva and Teixeira (arXiv:1108.4396) showed that the structure constants of a Lie algebra are the solution of a system of linear equations provided a certain subset of the structure constants are given a-priori. Here it is noted that Lie algebras generated in this way are solvable and their derived subalgebras are Abelian if the system of linear equations considered by Paiva and Teixeira is not degenerate. An efficient numerical algorithm for the calculation of their structure constants is described.