Nambu-Lie Groups
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We extend the Nambu bracket to 1-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplicative Nambu structure. A Lie group G with a Nambu structure P is a Nambu-Lie group iff P=0 at the unit and the Nambu bracket of left (right) invariant forms is left (right) invariant. We define a corresponding notion of a Nambu-Lie algebra. We give several examples of Nambu-Lie groups and algebras.
17 pages, LaTex
Mathematics - Differential Geometry, Lie algebra, Infinite-dimensional Lie groups and their Lie algebras: general properties, 22 E 99, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Poisson manifolds; Poisson groupoids and algebroids, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, 58 F 05; 22 E 99, 1-forms, Nambu-Lie group, FOS: Mathematics, Nambu bracket, Symplectic Geometry (math.SG), 58 F 05
Mathematics - Differential Geometry, Lie algebra, Infinite-dimensional Lie groups and their Lie algebras: general properties, 22 E 99, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Poisson manifolds; Poisson groupoids and algebroids, Differential Geometry (math.DG), Mathematics - Symplectic Geometry, 58 F 05; 22 E 99, 1-forms, Nambu-Lie group, FOS: Mathematics, Nambu bracket, Symplectic Geometry (math.SG), 58 F 05
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