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Xiaomin Tang

Publications and source records attributed to Xiaomin Tang.

14 recordsLinked to original sources
arXiv2026

Carleson measures, tent embeddings, and Volterra-type integral operators on the unit ball

In this paper, we establish a sharp comparison between Carleson-cube and Bergman-metric-ball conditions on the open unit ball $\B$ and combine it with a Berezin-type characterization to prove embedding theorems for Besov spaces and Bergman spaces on $\B$ into logarithmic tent spaces in the Bergman metric. As applications, we characterize the boundedness, compactness, and essential norms of the Volterra-type integral operators $T_g$ and $I_g$ acting from the Besov space $B_t(\B)$ to the general function space $F(p,q,s)$.

math.FA↗
arXiv2026

The Uncertainty Principles of Quaternion Fractional Fourier Transform

In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give the UP for QFrFT in both the spatial and directional domains, providing a more precise condition for equality, example is given to verify the results. Furthermore, we extend the time-frequency UP to a frequency-frequency setting.

math.CV↗
arXiv2023

Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time

Transposed Poisson structures on the Schrödinger algebra in $(n+1)$-dimensional space-time of Schrödinger Lie groups are described. It was proven that the Schrödinger algebra $\mathcal{S}_{n}$ in case of $n\neq 2$ does not have non-trivial $\frac{1}{2}$-derivations and as it follows it does not admit non-trivial transposed Poisson structures. All $\frac{1}{2}$-derivations and transposed Poisson structures for the algebra $\mathcal{S}_{2}$ are obtained. Also, we proved that the Schrödinger algebra $\mathcal{S}_{2}$ admits a non-trivial ${\rm Hom}$-Lie structure.

math.RA↗
arXiv2022

2-local derivations and biderivations of $\frak{sl}(2)$ on all simple modules

This paper generalizes the concepts of 2-local derivations and biderivations (without the skewsymmetric condition) of a finite-dimensional Lie algebra from the adjoint module to any finite-dimensional module, and determines all 2-local derivations and biderivations of the 3-dimensional complex simple Lie algebra $\frak{sl}(2)$ on its any finite-dimensional simple module.

math.RT↗
arXiv2020

2-Local derivations on the W-algebra W(2,2)

The present paper is devoted to study 2-local derivations on W-algebra $W(2,2)$ which is an infinite-dimensional Lie algebras with some out derivations. We prove that all 2-local derivations on the W-algebra $W(2,2)$ are derivation. We also give a complete classification of the 2-local derivation on the so called thin Lie algebra and prove that it admits a lots of 2-local derivations which are not derivations.

math.RA↗
arXiv2020

Modules of polynomial Rota-Baxter Algebras and matrix equations

The all Rota-Baxter algebra structures on the polynomial algebra $R={\bf k}[x]$ are well known. We study the finite dimensional modules of polynomial Rota-Baxter algebras $(\bfk[x],P)$ or $(x {\bf k} [x],P)$ of weight nonzero since some cases of weight zero have been studied. The main result shows that every module over the polynomial Rota-Baxter algebra $(\bfk[x],P)$ or $(x {\bf k} [x],P)$ is equivalent to the modules over a plane ${\bf k}\langle x,y \rangle/ I$ where $I$ is some ideal of free algebra ${\bf k}\langle x,y \rangle$. Furthermore, we provide the classification of modules of polynomial Rota-Baxter algebras of weight nonzero through solution to some matrix equation.

math.RT↗
arXiv2018

Biderivations and commutative post-Lie algebra structures on the Lie algebra W(a,b)

For $a,b\in \mathbb{C}$, the Lie algebra $\mathcal{W}(a,b)$ is the semidirect product of the Witt algebra and a module of the intermediate series. In this paper, all biderivations of $\mathcal{W}(a,b)$ are determined. Surprisingly, these Lie algebras have symmetric (and skewsymmetric) non-inner biderivations. As an applications, commutative post-Lie algebra structures on $\mathcal{W}(a,b)$ are obtained.

math.RA↗
arXiv2017

Post-Lie algebra structures on the Witt algebra

In this paper, we characterize the graded post-Lie algebra structures and a class of shifting post-Lie algebra structures on the Witt algebra. We obtain some new Lie algebras and give a class of their modules. As an application, the homogeneous Rota-Baxter operators and a class of non-homogeneous Rota-Baxter operators of weight $1$ on the Witt algebra are studied.

math.RA↗
arXiv2017

Biderivations of the twisted Heisenberg-Virasoro algebra and their applications

In this paper, the biderivations without the skew-symmetric condition of the twisted Heisenberg-Virasoro algebra are presented. We find some non-inner and non-skew-symmetric biderivations. As applications, the characterizations of the forms of linear commuting maps and the commutative post-Lie algebra structures on the twisted Heisenberg-Virasoro algebra are given. It also is proved that every biderivation of the graded twisted Heisenberg-Virasoro left-symmetric algebra is trivial.

math.RA↗
arXiv2016

Biderivations of finite dimensional complex simple Lie algebras

In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.

math.RA↗
arXiv2016

Block type Lie algebras and their representations

Block type Lie algebras have been studied by many authors in the latest twenty years. In this paper, we will study a class of more general Block type Lie algebra $\mathcal{B}(p,q)$, which is a class of infinite-dimensional Lie algebra by using the generalized Balinskii-Novikov's construction method to Witt type Novikov algebra. We study the representation theory for $\mathcal{B}(p,q)$. We classify quasifinite irreducible highest weight $\mathcal{B}(p,q)$-module. We also prove that any quasifinite irreducible module of Block type Lie algebras $\mathcal{B}(p,q)$ is either a highest or lowest weight module, or else a uniformly bounded module. This paper can be considered as a generalization of the related literatures.

math.RT↗