SPLIT

PASCAL programs for identification of Lie algebras. II: SPLIT - a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums. The program SPLIT (based on PASCAL) contains 161 subprograms (8000 lines) and determines a decomposition of a given Lie algebra L into the direct sum of smaller Lie algebras, if such a decomposition exists. The decomposition algorithm is basing on the fact that the adjoint representation (as matrix representation) of L is decomposable if and only if there are non-trivial idempotents commuting with the representation. Therefore the algorithm at first calculates the centralizer of ad and then its Jacobson radical. After forming the quotient algebra there are good criteria for decomposability. For the theoretical explanation see also Zbl 0668.17004. Several examples of dimension up to nine are presented.

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References in zbMATH (referenced in 9 articles , 1 standard article )

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  1. Šnobl, L.; Winternitz, P.: Solvable Lie algebras with Borel nilradicals (2012)
  2. Winternitz, Pavel: Lie groups, singularities and solutions of nonlinear partial differential equations (2003)
  3. Bracken, P.; Grundland, A. M.: Symmetry properties and explicit solutions of the generalized Weierstrass system (2001)
  4. Clarkson, Peter A.; Winternitz, Pavel: Symmetry reduction and exact solutions of nonlinear partial differential equations (1999)
  5. MacCallum, M. A. H.: On the classification of the real four-dimensional Lie algebras (1999)
  6. Reid, Gregory J.: Finding abstract Lie symmetry algebras of differential equations without integrating determining equations (1991)
  7. Winternitz, P.: Group theory and exact solutions of partially integrable differential systems (1990)
  8. Rand, D. W.: PASCAL programs for identification of Lie algebras. III: Levi decomposition and canonical basis (1987)
  9. Rand, D. W.; Winternitz, P.; Zassenhaus, Hans: PASCAL programs for identification of Lie algebras. II: SPLIT - a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums (1987)