Let G = H × R be a semidirect product Lie group. We reduce the problem of deciding which indecomposable representations of G may be realized in subquotients of spaces of sections of vector bundles over infinitesimal neighborhoods of orbits of H in the dual of R, to a problem involving only representations of the H-stabilizers of the orbits.

We construct generic Picard-Vessiot extensions for linear algebraic groups which are isomorphic to the semidirect product of a connected group G by an arbitrary finite group H, where the adjoint H-action on the Lie algebra of G is faithful.

The Landau^Lifshitz equation is derived as the reduction of a geodesic £ow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages. Mathematics Subject Classi¢cations (2000): 70H05, 35L70, 58B25. Key words: Landau^Lifshitz equations, Lie^Poisson reduction, geodesic £ow, momentum. The La...

In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is ba...

Here we carry out computations that help clarify the La-grangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the the

We develop a multi-scale theory for group of diffeomorphisms based on previous works [BGBHR11, RVW11, SNLP11, SLNP11]. The purpose of the paper is to develop in details a variational approach for multiscale on diffeomorphisms and to generalize to several scales the semidirect product of group representation. We also show that the approaches presented in [SNLP11, SLNP11] and the mixture of kerne...

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.

In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer derivations. We then present some examples for which these conditions hold.

We show that 40 is the maximum number of points of a cap in AG(4, 4). Up to semi-linear transformations there is only one such 40-cap. Its group of automorphisms is a semidirect product of an elementary abelian group of order 16 and the alternating group A5.