We present an extension of the methods of classical Lie group analysis of diierential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau's theory of algebras of generalized functions. We show that under some mild conditions on the diierential equations, symmetries of classical solutions r...

We study hermitian structures, with respect to the standard neutral metric on the cotangent bundle T ∗G of a 2n-dimensional Lie group G, which are left invariant with respect to the Lie group structure on T ∗G induced by the coadjoint action. These are in one-to-one correspondence with left invariant generalized complex structures on G. Using this correspondence and results of [8] and [10], it ...

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of...

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propose a method to obtain generalized Lie bialgebras. It is a generalization of t...

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...

The continuous general linear group in n dimensions can be decomposed into two Lie groups: (1) an n(n-1) dimensional ‘Markov type’ Lie group that is defined by preserving the sum of the components of a vector, and (2) the n dimensional Abelian Lie group, A(n), of scaling transformations of the coordinates. With the restriction of the first Lie algebra parameters to non-negative values, one obta...

1. Arnold M., Brüls O., Cardona A., 2015, Error analysis of generalized-α Lie group time integration methods for constrained mechanical systems, Numerische Mathematik, 129, 149-179. CrossRef Google Scholar

This work studies the dynamic modeling method for a service robot with Omnidirectional Mobile ManipulatorS configuration. Based on screw theory, Lie group notations, reciprocal product of twist and wrench, and Jourdain principle, the robot’s motion equations including the whole body manipulation are formulated with left invariant representation. A legible and canonical dynamic model representin...