Lie algebras are extended to the affine case using the heap operation, giving them a
definition that is not dependent on the unique element 0, such that they still adhere to …

It has been a long standing question how to extend, in the finite-dimensional setting, the
canonical Poisson bracket formulation from classical mechanics to classical field theories, in …

Affine Hamiltonians are defined in the paper and their study is based especially on the fact
that in the hyperregular case they are dual objects of Lagrangians defined on affine bundles …

Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are
studied. These include general normalised affine matrices, special normalised affine …

It is shown that any Lie affgebra, that is an algebraic system consisting of an affine space
together with a bi-affine bracket satisfying affine versions of the antisymmetry and Jacobi …

Special Normalised Affine Matrices: An Example of a Lie Affgebra | SpringerLink Skip to main
content Advertisement SpringerLink Account Menu Find a journal Publish with us Track your …

We show that the category of affine bundles over a smooth manifold M is equivalent to the
category of affine spaces modelled on projective finitely generated C^\infty (M)-modules …

A new setting that allows a new definition of a time dependent Lagrangian of higher order is
considered. Canonical constructions of some connections and of a semispray, associated …

We present the notion of a filtered bundle as a generalization of a graded bundle. In
particular, we weaken the necessity of the transformation laws for local coordinates to …

A new setting that allows a new definition of a time dependent Lagrangian of higher order is
considered. Canonical constructions of some connections and of a semispray, associated …