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Results tagged with lie-algebras
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user 61197
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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Nonlinear Poisson brackets associated with nilpotent (matrix) Lie algebras?
With every finite-dimensional Lie algebra $\mathfrak{g}$ one can associate a linear Poisson bracket on $\mathfrak{g}^\ast$. With some more restrictions on $\mathfrak{g}$ and some extra ingredients, th …
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Nontrivial Poisson relations for affine Poisson algebras
Lie ideals in Lie algebras also define Poisson ideals of the associated Lie-Poisson structure.
Consider the Lie-Poisson structure associated to the Lie algebra of upper-triangular $3\times 3$ matrice …
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