We show how the Newton-Hooke (NH) symmetries, representing a nonrelativistic version of de-Sitter symmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class of accelerations linear in time. We study the Cartan-Maurer one-forms corresponding to such enlarged NH symmetry group and by using cohomological methods we determine the general 2-parameter (in D = ...

Quantum groups play a role of symmetries of integrable theories in two dimensions. They may be detected on the classical level as Poisson-Lie symmetries of the corresponding phase spaces. We discuss specifically the Wess-Zumino-Witten conformally invariant quantum field model combining two chiral parts which describe the leftand right-moving degrees of freedom. On one hand side, the quantum gro...

We construct a sequence of nilpotent BRST charges in RNS superstring theory, based on new gauge symmetries on the worldsheet, found in this paper. These new local gauge symmetries originate from the global nonlinear space-time α-symmetries, shown to form a noncommutative ground ring in this work. The important subalgebra of these symmetries is U(3)×X6, where X6 is solvable Lie algebra consistin...

In 1969, Murray Gell-Mann won the nobel prize in physics “for his contributions and discoveries concerning the classification of elementary particles and their interactions.” He is the scientist who first used the word quark, and he was the first to describe the SU3(C) flavor symmetry of the hadrons. By organizing the particles according to the root system of the lie algebra su3(C) associated t...

Abstract The Lie symmetry analysis is adopted to the (2 + 1)-dimensional dispersionless B-type Kadomtsev–Petviashvili (dBKP) equation. combination of and symbolic computing methods proves that algebra infinitesimal dBKP equation depends on four independent arbitrary functions one parameter. reduced classes for deriving commutative relations, group invariant solutions conservation laws, optimal ...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

We study the Lie point symmetries and similarity transformations for partial differential equations of nonlinear one-dimensional magnetohydrodynamic system with Hall term known as HMHD system. For this 1+1 we find that is invariant under action a seventh dimensional algebra. Furthermore, optimal derived while invariants are applied derivation transformations. present different kinds oscillating...

Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almostparabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)C. We consider nonhermitian represen...

Representation theory. Let us try to study a given object X through vector spaces V associated naturally to it. The symmetries S of X can form a group or more generally some kind of an algebra usually related to a group (Lie algebra, quantum group,...). The Vector space V inherits the symmetries of X, and they act on V by linear operators. This is what one means by “V is a representation of the...

We introduce a higher dimensional generalization of the affine Kac-Moody algebra using language factorization algebras. In particular, on any complex manifold there is currents associated to Lie algebra. classify local cocycles these current algebras, and compare them central extensions algebras recently proposed by Faonte-Hennion-Kapranov. A goal this paper witness as symmetries class holomorp...