Classification of solvable lie algebras

Experimental Mathematics

Volumn 14, Issue 1, 2005, Pages 15-25

  De Graaf, W A ^a  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

Author keywords

Classification; Gr bner bases; Lie algebras

Indexed keywords

EID: 22544462820     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2005.10128911     Document Type: Article

References (10)

1. E. R. Berlekamp. Algebraic Coding Theory. New York: McGraw-Hill, 1968.
2. W. Bosma, J. Cannon, and C. Playoust. “The Magma Algebra System. I. The User Language.” J. Symbolic Comput., 24: 3/4 (1997), 235-265.
3. D. Cox, J. Little, and D. O’Shea. Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. New York-Heidelberg-Berlin: Springer Verlag, 1992.
4. W. A. de Graaf. Lie Algebras: Theory and Algorithms, North-Holland Mathematical Library, 36. Amsterdam: Elsevier Science, 2000.
5. V. P. Gerdt and W. Lassner. “Isomorphism Verification for Complex and Real Lie Algebras by Gröbner Basis Technique.” In Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, edited by N. H. Ibragimov et al., pp. 245-254. Dordrecht: Kluwer Academic Publishers, 1993.
6. B. Hartley and T. O. Hawkes. Rings, Modules and Linear Algebra. A Further Course in Algebra Describing the Structure of Abelian Groups and Canonical Forms of Matrices through the Study of Rings and Modules. London: Chapman and Hall Ltd., 1970.
7. G. M. Mubarakzjanov. “Classification of Real Structures of Lie Algebras of Fifth Order.” Izv. Vysš. Učebn. Zaved. Matematika 3: 34 (1963), 99-106.
8. G. M. Mubarakzjanov. “Classification of Solvable Lie Algebras of Sixth Order with a Non-Nilpotent Basis Element.” Izv. Vysš. Učebn. Zaved. Matematika 4: 35 (1963), 104-116.
9. J. Patera and H. Zassenhaus. “Solvable Lie Algebras of Dimension ≤ 4 over Perfect Fields.” Linear Algebra Appl. 142 (1990), 1-17.
10. 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 Appl. 109 (1988), 197-246.