Asian Journal of Mathematics最新文献_第8页

Representations and modules of Rota–Baxter algebras Rota-Baxter代数的表示与模

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-05-04 DOI: 10.4310/ajm.2021.v25.n6.a3

Li Guo, Zongzhu Lin

引用次数: 15

Critical $L$-values for some quadratic twists of gross curves 粗曲线的某些二次扭曲的临界$L$-值

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-04-18 DOI: 10.4310/ajm.2020.v24.n2.a4

A. Dkabrowski, Tomasz Jkedrzejak, L. Szymaszkiewicz

引用次数: 2

Algebraic properties of bounded killing vector fields 有界杀伤向量场的代数性质

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-04-18 DOI: 10.4310/ajm.2021.v25.n2.a4

Ming Xu, Yu.G. Nikonorov

{"title":"Algebraic properties of bounded killing vector fields","authors":"Ming Xu, Yu.G. Nikonorov","doi":"10.4310/ajm.2021.v25.n2.a4","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n2.a4","url":null,"abstract":"In this paper, we consider a connected Riemannian manifold $M$ where a connected Lie group $G$ acts effectively and isometrically. Assume $Xinmathfrak{g}=mathrm{Lie}(G)$ defines a bounded Killing vector field, we find some crucial algebraic properties of the decomposition $X=X_r+X_s$ according to a Levi decomposition $mathfrak{g}=mathfrak{r}(mathfrak{g})+mathfrak{s}$, where $mathfrak{r}(mathfrak{g})$ is the radical, and $mathfrak{s}=mathfrak{s}_coplusmathfrak{s}_{nc}$ is a Levi subalgebra. The decomposition $X=X_r+X_s$ coincides with the abstract Jordan decomposition of $X$, and is unique in the sense that it does not depend on the choice of $mathfrak{s}$. By these properties, we prove that the eigenvalues of $mathrm{ad}(X):mathfrak{g}rightarrowmathfrak{g}$ are all imaginary. Furthermore, when $M=G/H$ is a Riemannian homogeneous space, we can completely determine all bounded Killing vector fields induced by vectors in $mathfrak{g}$. We prove that the space of all these bounded Killing vector fields, or equivalently the space of all bounded vectors in $mathfrak{g}$ for $G/H$, is a compact Lie subalgebra, such that its semi-simple part is the ideal $mathfrak{c}_{mathfrak{s}_c}(mathfrak{r}(mathfrak{g}))$ of $mathfrak{g}$, and its Abelian part is the sum of $mathfrak{c}_{mathfrak{c}(mathfrak{r}(mathfrak{g}))} (mathfrak{s}_{nc})$ and all two-dimensional irreducible $mathrm{ad}(mathfrak{r}(mathfrak{g}))$-representations in $mathfrak{c}_{mathfrak{c}(mathfrak{n})}(mathfrak{s}_{nc})$ corresponding to nonzero imaginary weights, i.e. $mathbb{R}$-linear functionals $lambda:mathfrak{r}(mathfrak{g})rightarrow mathfrak{r}(mathfrak{g})/mathfrak{n}(mathfrak{g}) rightarrowmathbb{R}sqrt{-1}$, where $mathfrak{n}(mathfrak{g})$ is the nilradical.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":"195 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Lagrangian Floer homology on symplectic blow ups 辛爆破上的拉格朗日Floer同调

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-04-08 DOI: 10.4310/ajm.2020.v24.n2.a3

Andr'es Pedroza

引用次数: 1

An $varepsilon$-regularity theorem for line bundle mean curvature flow 线束平均曲率流的$varepsilon$正则性定理

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-04-04 DOI: 10.4310/ajm.2022.v26.n6.a1

Xiaoling Han, Hikaru Yamamoto

引用次数: 5

Metrics and compactifications of Teichmüller spaces of flat tori 平面环面的Teichmüller空间的度量与紧性

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-03-26 DOI: 10.4310/ajm.2021.v25.n4.a2

M. Greenfield, L. Ji

引用次数: 5

Gauss–Kronecker curvature and equisingularity at infinity of definable families 可定义族无穷远处的Gauss–Kronecker曲率和等奇异性

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-03-19 DOI: 10.4310/ajm.2021.v25.n6.a2

N. Dutertre, V. Grandjean

引用次数: 3

Moving Seshadri constants, and coverings of varieties of maximal Albanese dimension 移动的Seshadri常数和极大Albanese维数变化的复盖

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-02-11 DOI: 10.4310/ajm.2021.v25.n2.a8

L. D. Cerbo, L. Lombardi

引用次数: 7

Divisorial instability and Vojta’s main conjecture for $mathbb{Q}$-Fano varieties $mathbb{Q}$-Fano的分不稳定性和Vojta的主要猜想

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-01-23 DOI: 10.4310/ajm.2020.v24.n6.a3

Nathan Grieve

引用次数: 1

Formality of Floer complex of the ideal boundary of hyperbolic knot complement 双曲结补的理想边界花复合体形式

IF 0.6 4区数学

Asian Journal of Mathematics Pub Date : 2019-01-08 DOI: 10.4310/ajm.2021.v25.n1.a7

Youngjin Bae, Seonhwa Kim, Y. Oh

{"title":"Formality of Floer complex of the ideal boundary of hyperbolic knot complement","authors":"Youngjin Bae, Seonhwa Kim, Y. Oh","doi":"10.4310/ajm.2021.v25.n1.a7","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n1.a7","url":null,"abstract":"This is a sequel to the authors' article [BKO](arXiv:1901.02239). We consider a hyperbolic knot $K$ in a closed 3-manifold $M$ and the cotangent bundle of its complement $M setminus K$. We equip $M setminus K$ with a hyperbolic metric $h$ and its cotangent bundle $T^*(M setminus K)$ with the induced kinetic energy Hamiltonian $H_h = frac{1}{2} |p|_h^2$ and Sasakian almost complex structure $J_h$, and associate a wrapped Fukaya category to $T^*(Msetminus K)$ whose wrapping is given by $H_h$. We then consider the conormal $nu^*T$ of a horo-torus $T$ as its object. We prove that all non-constant Hamiltonian chords are transversal and of Morse index 0 relative to the horo-torus $T$, and so that the structure maps satisfy $widetilde{mathfrak m}^k = 0$ unless $k neq 2$ and an $A_infty$-algebra associated to $nu^*T$ is reduced to a noncommutative algebra concentrated to degree 0. We prove that the wrapped Floer cohomology $HW(nu^*T; H_h)$ with respect to $H_h$ is well-defined and isomorphic to the Knot Floer cohomology $HW(partial_infty(M setminus K))$ that was introduced in [BKO] for arbitrary knot $K subset M$. We also define a reduced cohomology, denoted by $widetilde{HW}^d(partial_infty(M setminus K))$, by modding out constant chords and prove that if $widetilde{HW}^d(partial_infty(M setminus K))neq 0$ for some $d geq 1$, then $K$ cannot be hyperbolic. On the other hand, we prove that all torus knots have $widetilde{HW}^1(partial_infty(M setminus K)) neq 0$.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41689793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4