Lie algebroid structures on a class of affine bundles
نویسندگان
چکیده
منابع مشابه
Lie algebroid structures on a class of affine bundles
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over IR. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the theory of Lagrangian systems on Lie algebroids. An extensive discussion is given of a way one can think of forms acting on sections of the affine bundle. It is further shown th...
متن کاملLie algebroid structures and Lagrangian systems on affine bundles
As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.
متن کاملLie Brackets on Affine Bundles
Natural analogs of Lie brackets on affine bundles are studied. In particular, a close relation to Lie algebroids and a duality with certain affine analog of Poisson structure is established as well as affine versions of the complete lift and the Cartan exterior calculus.
متن کاملNoncomplete Affine Structures on Lie Algebras of Maximal Class
Every affine structure on Lie algebra g defines a representation of g in aff(Rn). If g is a nilpotent Lie algebra provided with a complete affine structure then the corresponding representation is nilpotent. We describe noncomplete affine structures on the filiform Lie algebra Ln. As a consequence we give a nonnilpotent faithful linear representation of the 3-dimensional Heisenberg algebra. 200...
متن کاملJacobi structures on affine bundles
We study affine Jacobi structures (brackets) on an affine bundle π : A→M , i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-to-one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. In the case rank A = 0, it is shown that there is a one-t...
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: Journal of Mathematical Physics
سال: 2002
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1510958