Displaying similar documents to “Invariant convex sets and functions in Lie algebras.”

Reductions and conservation laws for BBM and modified BBM equations

Maryam Khorshidi, Mehdi Nadjafikhah, Hossein Jafari, Maysaa Al Qurashi (2016)

Open Mathematics

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In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations....

Invariant orders in Lie groups

Neeb, Karl-Hermann

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[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group G admits a continuous invariant order if and only if its Lie algebra L ( G ) contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If G is solvable and simply connected then all pointed invariant cones W in L ( G ) are global in G (a Lie wedge W ⊂ L ( G ) ...