一类模李代数的导子代数(英文)

本文通过构造一类模线状李代数,求出了它的导子代数,并且证明这个导子代数是可解但不完备的模李代数.这将有利于研究一般模线状李代数的结构.     

Lie Higher Derivations on Nest Algebras

Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = （Ln）n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln（A） ： Tn（A） ＋ hn（A）I for all A ∈ AlgN, where （Tn）n∈N is a higher derivation and （hn）n∈N is a sequence of additive functionals satisfying hn（[A,B]） = 0 for all A,B ∈ AlgN and all n ∈ N.     

一类广义W型李超代数

构造了一类有限维广义Cartan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

Lie symmetry analysis, conservation laws and exact solutions of fourth-order time fractional Burgers equation

In this paper, the fourth-order time fractional Burgers equation has been investigated, which can be used to describe gas dynamics and traffic flow. By employing the Lie group analysis method, the invariance properties of the equation are provided. With the aid of the sub-equation method, a new type of explicit solutions are well constructed with a detailed derivation. Furthermore, based on the power series theory, we investigate its approximate analytical solutions. Finally, its conservation laws with two kinds of independent variables are performed by making use of the nonlinear self-adjointness method.     

Exact solutions via invariant approach for Black‐Scholes model with time‐dependent parameters

We analyze the Black‐Scholes model with time‐dependent parameters, and it is governed by a parabolic partial differential equation (PDE). First, we compute the Lie symmetries of the Black‐Scholes model with time‐dependent parameters. It admits 6 plus infinite many Lie symmetries, and thus, it can be reduced to the classical heat equation. We use the invariant criteria for a scalar linear (1+1) parabolic PDE and obtain 2 sets of equivalence transformations. With the aid of these equivalence transformations, the Black‐Scholes model with time‐dependent parameters transforms to the classical heat equation. Moreover, the functional forms of the time‐dependent parameters in the PDE are determined via this method. Then we use the equivalence transformations and known solutions of the heat equation to establish a number of exact solutions for the Black‐Scholes model with time‐dependent parameters.     

Exact solutions of the time fractional nonlinear Schrödinger equation with two different methods

In the present paper, exact solutions of fractional nonlinear Schrödinger equations have been derived by using two methods: Lie group analysis and invariant subspace method via Riemann‐Liouvill derivative. In the sense of Lie point symmetry analysis method, all of the symmetries of the Schrödinger equations are obtained, and these operators are applied to find corresponding solutions. In one case, we show that Schrödinger equation can be reduced to an equation that is related to the Erdelyi‐Kober functional derivative. The invariant subspace method for constructing exact solutions is presented for considered equations.     

Free 2-step nilpotent Lie algebras and indecomposable representations

Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V)?=?V⊕Λ²(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations of the solvable Lie algebra 𝔤?=??x??L(V), where x acts on V via an arbitrary invertible Jordan block.