W. A. de Graaf
- 1.R. E. Beck, B. Kolman and I. N. Stewart, Computing the Structure of a Lie Algebra, in: R. E. Beck and B. Kolman eds., Computers in Non-associative Rings and Algebra.s, Academic Press, New York, 167-188 (1977).Google Scholar
- 2.G. Birkhoff, Representability of Lie Algebras and Lie Groups by Matrices, Annals of Mathematics 38 526- 532 (1937).Google ScholarCross Ref
- 3.N. Bourbaki, Groupes et Algtbres de Lie, Chap. I, Hermann, Paris, (1960).Google Scholar
- 4.\V. A. de Graaf, G. Ivanyos, At Kiironya and L. Rdnyai, Computing Levi Decompositions in Lie Algebras, to appear in Applicable Algebra in Engineering, Communication and Computing.Google Scholar
- 5.N. Ja,:obson, Lie Algebras, Dover, New York, (1979).Google Scholar
- 6.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 Alg. Appl. 109 197-246 (1988).Google ScholarCross Ref
Index Terms
- Constructing faithful matrix representations of Lie algebras
Recommendations
Computing matrix representations of filiform lie algebras
CASC'10: Proceedings of the 12th international conference on Computer algebra in scientific computingIn this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, gn, formed of n×n strictly upper-triangular matrices. More concretely, we search the lowest natural ...
Minimal faithful upper-triangular matrix representations for solvable Lie algebras
The existence of matrix representations for any given finite-dimensional complex Lie algebra is a classic result on Lie Theory. In particular, such representations can be obtained by means of an isomorphic matrix Lie algebra consisting of upper-...
Constructing algebraic groups from their Lie algebras
A connected algebraic group in characteristic 0 is uniquely determined by its Lie algebra. In this paper algorithms are given for constructing an algebraic group in characteristic 0, given its Lie algebra. In particular, this leads to an algorithm for ...
Comments