A NOTE ON NONDEGENERATE POISSON STRUCTURE
نویسندگان
چکیده
The Schouten-Nijenhuis bracket on the module of K\"ahler differentials is introduced. We recover Lichnerowicz's notion Poisson manifold by using universal property derivations. prove that a nondegenerate structure corresponds exactly to symplectic structure. Finally, we explore Hamiltonian vector fields in terms
منابع مشابه
A Note on n-ary Poisson Brackets
A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n− 2 covectors are decomposable. In the last years, several authors have studied g...
متن کاملA Note on n - ary Poisson BracketsbyPeter
A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are deened by a decomposable 3-vector eld. The key point is the proof of a lemma which tells that an n-vector (n 3) is decomposable ii all its contractions with up to n ? 2 covectors are decomposable. In the last years, several authors have studied genera...
متن کاملA Note on Poisson Lie Algebroids
The Lie algebroid [10] is a generalization of both concepts of Lie algebra and integrable distribution, being a vector bundle (E, π, M) with a Lie bracket on his space of sections with properties very similar to those of a tangent bundle. The Poisson manifolds are the smooth manifolds equipped with a Poisson bracket on their ring of functions. I have to remark that the cotangent bundle of a Poi...
متن کاملA Note on Poisson Symmetric Spaces
We introduce the notion of a Poisson symmetric space and the associated infinitesimal object, a symmetric Lie bialgebra. They generalize corresponding notions for Lie groups due to V. G. Drinfel’d. We use them to give some geometric insight to certain Poisson brackets that have appeared before in the literature. 1 Motivation Let us recall briefly the best-known examples of Poisson manifolds. Th...
متن کاملA Note on Proper Poisson Actions
We show that the fixed point set of a proper action of a Lie group G on a Poisson manifold M by Poisson automorphisms has a natural induced Poisson structure and we give several applications.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2022
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.37418/amsj.11.11.8