Left-Symmetric Superalgebra Structures on a Super Virasoro Type Algebra

In this note we classify the compatible left-symmetric superalgebra structures over a super Virasoro type algebra, whose even part is the centerless twisted Heisenberg–Virasoro algebra, with some natural grading conditions.

Classical Lie symmetries and similarity reductions of the (2 + 1)-dimensional dispersive long wave system

In the present work, classical Lie symmetry method is adopted to obtain the Lie symmetries and similarity reductions of the (2 + 1)-dimensional dispersive long wave equation. We also demonstrate that the symmetry algebra of this equation is an infinte dimensional, together with Kac–Moody–Virasoro type subalgebras.

Finite irreducible modules of Lie conformal algebras 𝒲(a,b) and some Schrödinger–Virasoro type Lie conformal algebras

Lie conformal algebras [Formula: see text] are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we first give a complete classification of all finite nontrivial irreducible conformal modules of [Formula: see text]. It is shown that all such modules are of rank one. Moreover, with a similar method, all finite nontrivial irreducible conformal modules of Schrödinger–Virasoro type Lie conformal algebras [Formula: see text] and [Formula: see text] are characterized.

Dual Lie Bialgebra Structures of Twisted Schrödinger-Virasoro Type

In this paper, the structures of dual Lie bialgebras of twisted Schrödinger-Virasoro type are investigated. By studying the maximal good subspaces, we determine the dual Lie coalgebras of the twisted Schrödinger-Virasoro algebras. Then based on this, we construct the dual Lie bialgebra structures of this type. As by-products, four new infinite dimensional Lie algebras are obtained.

A class of Schrödinger–Virasoro type Lie conformal algebras

In this paper, a class of Lie conformal algebras associated to a Schrödinger–Virasoro type Lie algebra is constructed, which is nonsimple and can be regarded as an extension of the Virasoro conformal algebra. Then conformal derivations, second cohomology group with trivial coefficients and conformal modules of rank 1 of this Lie conformal algebra are investigated.

New Nonlinear Systems Admitting Virasoro-Type Symmetry Algebra and Group-Invariant Solutions

With the aid of symbolic computation by Maple, we extend the application of Virasoro-type symmetry prolongation method to coupled systems with two-component nonlinear equations. New nonlinear systems admitting infinitely dimensional centerless Virasoro-type symmetry algebra are constructed. Taking one of them as an example, we present some group-invariant solutions to one of the new model systems.