Nonlinear Galilei-Invariant PDEs with Infinite-Dimensional Lie Symmetry

Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs

We construct, for any given ` = 1 2 + N0, second-order nonlinear partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is obs...

Infinite dimensional backstepping for nonlinear parabolic PDEs

Modular invariant representations of infinite-dimensional Lie algebras and superalgebras.

In this paper, we launch a program to describe and classify modular invariant representations of infinite-dimensional Lie algebras and superalgebras. We prove a character formula for a large class of highest weight representations L(lambda) of a Kac-Moody algebra [unk] with a symmetrizable Cartan matrix, generalizing the Weyl-Kac character formula [Kac, V. G. (1974) Funct. Anal. Appl. 8, 68-70]...

Infinite Dimensional Lie Groups

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

Infinite-dimensional Lie algebras