We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

One considers a class of PDEs systems (1) equivalent to (8) and one determines the PDEs system (10) which defines the associated symmetry group. Particularly, for the Blair system (2)+(3) equivalent to (14), one finds the symmetry Lie group G (Theorem 5). One proves that the class of PDEs systems in the form (8)+(14′) which are invariant with respect to the Lie group G, is reduced to the Blair ...

The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that, from the knowledge of the BRST cohomology, it is possible to explicitly construct a further extension of the formalism containing all the observables of the th...

Infinitesimal bialgebras were introduced by Joni and Rota [J-R]. An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in such a way that the comultiplication is a derivation. In this paper we define infinitesimal Hopf algebras, develop their basic theory and present several examples. It turns out that many properties of ordinary Hopf algebras possess an infinitesimal versi...

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...

Abstract Studies on Non-linear evolutionary equations have become more critical as time evolves. Such are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used apply similarity reduction some a (3+1) dimensional nonlinear evolution...

We investigate the phase space of a typical model of (1+1) dimensional gravity (Jackiw-Teitelboim model with cylindrical topology) using its reformulation as a non abelian gauge theory based on the sl(2, IR) algebra. Modifying the conventional approach we argue that one should take the universal covering of SL(2, IR) rather than PSL(2, IR) as the gauge group of the theory. We discuss the conseq...