J C Ndogmo 2004 J. Phys. A: Math. Gen. 37 5635 doi:10.1088/0305-4470/37/21/009
Invariants of a semi-direct sum of Lie algebras
J C Ndogmo
Show affiliationsWe show that any semi-direct sum L of Lie algebras with Levi factor S must be perfect if the representation associated with it does not possess a copy of the trivial representation. As a consequence, all invariant functions of L must be Casimir operators. When 
, the number of invariants is given for all possible dimensions of L. Replacing the traditional method of solving the system of determining PDEs by the equivalent problem of solving a system of total differential equations, the invariants are found for all dimensions of the radical up to 5. An analysis of the results obtained is made, and this leads to a theorem on invariants of Lie algebras depending only on the elements of certain subalgebras.
- PACS
- MSC
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22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
- Subjects
- Dates
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Issue 21 (28 May 2004)
Received 13 February 2004, in final form 2 April 2004
Published 12 May 2004
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Invariants of a semi-direct sum of Lie algebras
J C Ndogmo 2004 J. Phys. A: Math. Gen. 37 5635
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