Frank Kutzschebauch, Andreas Lind
We prove that any Lie subgroup $G$ (with finitely many connected components) of an infinite-dimensional topological group $\mathcal G$ which is an amalgamated product of two closed subgroups, can be conjugated to one factor. We apply this result to classify Lie group actions on Danielewski surfaces by elements of the overshear group (up to conjugation).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Holomorphic automorphisms of Danielewski surfaces II -- structure of the overshear group
我们应用Nevanlinna理论代数簇Danielewski表面和调查他们的全纯自同构群。我们的主要结果是：已知在全纯自同构群的单位连通区稠密的过剪切群是自由的合并积。
On complete generators of certain Lie algebras on Danielewski surfaces
研究Danielewski曲面上多项式向量场的李代数，证明其由6个完全向量场生成，体积保持多项式向量场由有限个向量场生成，且存在由4个LND生成的子代数，其流作用在曲面上无限可迁。
We give a full description of the Lie algebra generated by locally nilpotent derivations (short LNDs) on smooth Danielewski surfaces $D_p$ given by $xy=p(z)$. In case $\mathrm{deg}(p)\geq 3$ it turns out to be not the whole Lie algebra $\mathrm{VF}_{alg}^ω(D_p)$ of volume preserving algebraic vector fields, thus answering a question posed by Lind and the first author. Also we show algebraic volume density property (short AVDP) for a certain homology plane, a homogeneous space of the form $SL_2 (\mathbb{C}) /N$, where $N$ is the normalizer of the maximal torus and another related example. At th…
For the special linear group $\mathrm{SL}_2(\mathbb{C})$ and for the singular quadratic Danielewski surface $x y = z^2$ we give explicitly a finite number of complete polynomial vector fields that generate the Lie algebra of all polynomial vector fields on them. Moreover, we give three unipotent one-parameter subgroups that generate a subgroup of algebraic automorphisms acting infinitely transitively on $x y = z^2$.
Holomorphic retracts in the Lie ball and the tetrablock
本文研究Lempert域中全纯收缩的性质，将其存在性与线性收缩关联，并给出三维Lie球与四块体中全纯收缩的完整描述。
In this paper we derive formulas for the Monge-Ampère measures of functions of the form $\log|Φ|_c$, where $Φ$ is a holomorphic map on a complex manifold $X$ of dimension $n$ with values in $\mathbb{C}^{n+1}\setminus\{0\}$ and $|\cdot|_c$ is the Lie norm on $\mathbb{C}^{n+1}$.
Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains
本文证明了包括所有连通实半单群在内的一大类李群（含许多非线性李群）均可实现为仿射复空间有界域的全纯自同构群，推广了1990年关于连通线性李群的结论。
The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function $\tilde f:L_n\to \C$ on the Lie ball $L_n$ in $\C^n$ with its monogenic counterpart $f:B_1(0)\to \C^{n+1}$ via the formula $\tilde f(z) = \int_{S^n}G_\om(z)\bs n(\om)f(\om)\,dμ(\om)$, $z\in L_n.$ The inverse map $\tilde f\mapsto f$ is constructed here using the Cauchy-Hua formula for the Lie ball following the work of M. Morimoto \cite{Mori2}.
Let $\mathcal M$ be a compact complex supermanifold. We prove that the set $\mathrm{Aut}_{\bar 0}(\mathcal M)$ of automorphisms of $\mathcal M$ can be endowed with the structure of a complex Lie group acting holomorphically on $\mathcal M$, so that its Lie algebra is isomorphic to the Lie algebra of even holomorphic super vector fields on $\mathcal M$. Moreover, we prove the existence of a complex Lie supergroup $\mathrm{Aut}(\mathcal M)$ acting holomorphically on $\mathcal M$ and satisfying a universal property. Its underlying Lie group is $\mathrm{Aut}_{\bar 0}(\mathcal M)$ and its Lie super…
Cohomology of skew-holomorphic Lie algebroids
在复流形上引入了斜全纯李代数胚的概念，并探讨了与之相关的一些上同调理论，给出了各种全纯Poisson结构的例子.
Transversely Lie holomorphic foliations on projective spaces
证明了在射影空间上具有一般奇异性的一维叶理，在余维为1的代数子集的补中具有李群横截结构，是对数的，即，它是由具有单极点的闭一形式给出的余维一叶理的交集。如果在一个合适的仿射空间中只有一个奇点，则叶理是由一个线性对角向量场诱导的。
Borel-Weil Theory for Root Graded Banach-Lie groups
本文引入（弱）根分次Banach-李代数和相应的李群作为Banach代数$A$的类$\GL_n(A)$的自然推广或紧空间$X$到复半单李群$K$的连续映射的类$C(X,K)$的自然推广.研究了从抛物子群$P$的全纯Banach表示到$G/P$上齐次向量丛的全纯截面上$G$的表示的全纯诱导.我们的主要成果之一是代数表征的空间的部分是用来表明，这个空间实际上进行了自然的Banach结构，结果推广的有限维空间的部分全纯丛紧凑复杂的流形。本文还给出了（弱）根分次Banach-李群$G$的任何不可约全纯表示的几何实现，并证明了空间$G/P$上的所有全纯函数都是常数.
Projectively Invariant Cocycles of Holomorphic Vector Fields on an Open Riemann Surface
设$Σ$是开黎曼曲面，$Hol (Σ)$是$Σ.$上全纯向量场的李代数.在$Σ.$上固定一个射影结构（即局部$SL_2(C)-$结构）.给出了生成该上同调群的1-上圈的显式公式。
We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this result enables us to show that the second jet of a holomorphic vector field defined on a compact complex manifold M of dimension 3 cannot vanish at an isolated singular point provided that M carries more than a single holomorphic vector field.
Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms
本文提出一种仅基于李理论标准结论的李代数方法，为紧复齐性流形相关经典结论给出新证明，还提供了将典范阿贝尔李代数与紧李代数上可积复结构关联的方式，拓展了前人研究。
Holomorphic DIffeomorphisms of Semisimple Homogeneous Spaces
Stein流形X的密度性质意味着X的全纯超纯群是无限维的，并且在某种定义明确的意义上，尽可能大。证明了若G是伴随型复半单李群，K是约化子群，则G/K具有稠密性.这个定理是我们以前的一个结果的非平凡推广，它处理复半单李群的情形。我们还用ad hoc方法建立了其它复齐性空间的稠密性。最后，我们引入了一个提升方法，它把关于复流形的许多结果推广到复流形的覆盖空间上。
We prove that actions of complex reductive Lie groups on a holomorphic vector bundle over a complex compact manifold are locally extendable to its local moduli space.
Let K be a finite-dimensional, 1-connected complex Lie group, and let Σ_k=Σ- {p_1,\ldots,p_k\} be a compact connected Riemann surface Σ, from which we have extracted k > 0 distinct points. We study in this article the regular Frechet-Lie group O(Σ_k,K) of holomorphic maps from Σ_k to K and its central extension \widehat{O(Σ_k,K)}. We feature especially the automorphism groups of these Lie groups as well as the coadjoint orbits of \widehat{O(Σ_k,K)} which we link to flat K-bundles on Σ_k.
Suppose that a compact and connected Lie group $G$ acts on a complex Hodge manifold $M$ in a holomorphic and Hamiltonian manner, and that the action linearizes to a positive holomorphic line bundle $A$ on $M$. Then there is an induced unitary representation on the associated Hardy space and, if the moment map of the action is nowhere vanishing, the corresponding isotypical components are all finite dimensional. We study the asymptotic concentration behavior of the corresponding equivariant Szegö kernels near certain loci defined by the moment map.
Segre varieties and Lie symmetries
利用经典的S.Lie方法，我们得到了定义实解析超曲面的Segre族的全纯PDE系统的无穷小对称性的完整描述。这对CR几何的一些著名结果给出了新的证明。
Let $S$ be a complex reductive group acting holomorphically on a complex Lie group $N$ via holomorphic automorphisms. Let $K(S)\subset S$ be a maximal compact subgroup. The semidirect product $G := N\rtimes K(S)$ acts on $N$ via biholomorphisms. We give an explicit description of the isomorphism classes of $G$-equivariant almost holomorphic hermitian principal bundles on $N$. Under the assumption that there is a central subgroup $Z= \text{U}(1)$ of $K(S)$ that acts on $\text{Lie}(N)$ as multiplication through a single nontrivial character, we give an explicit description of the isomorphism cla…
Entire Functions on Lie Groups
本文研究了李群上的整体函数与复化李群上的全纯映射之间的对应关系，并通过复分析方法实现了严格变形量子化。
Infinite-dimensionality of the Automorphism Groups of Homogeneous Stein Manifolds
我们证明了维数大于1的Stein流形X的全纯自同构群是无限维的，只要X是复李群的全纯作用的齐性空间.
Integration of vector fields on smooth and holomorphic supermanifolds
给出了实超流形上任意光滑向量场（不一定是齐次的）流的存在性和唯一性的一个新的完备证明，并将这些结果推广到复超流形上全纯向量场的情形.此外，我们讨论了与超向量场相关的局部作用，并给出了几个例子和应用，例如，任意有限维李群的指数态射的构造。在第二个版本中，我们纠正了错别字，数字和其他小问题的呈现。我们在第3节和第4节中添加了参考文献。更多的细节在第4节的（4.2）部分给出，处理李群的指数态射。值得注意的是，我们现在给出两个结构的向量场导致的指数态射，我们证明了它的完整性，此外，我们刻画的指数态射的李群的指数映射从超点到给定的李群。
On localization in holomorphic equivariant cohomology
证明了一个附着在等变全纯向量丛的Atiyah代数体上的“全纯等变上同调”的局部化公式。这推广了Feng-Ma，Carrell-Liebermann，Baum-Bott和K. Liu的局部化公式。
Twistors, Holomorphic Disks, and Riemann Surfaces with Boundary
复流形Z中的全纯圆盘模空间，其边界被约束在极大全实子流形P中，最近被发现是许多几何上丰富的扭量对应的基础.本文的目的是开发一个通用的Fredholm正则性准则的全纯曲线与边界，然后显示如何适用于，特别是各种模问题的扭理论的兴趣。
Coherent state representations of the holomorphic automorphism group of a quasi-symmetric Siegel domain of type III
本文研究了III型拟对称Siegel域全纯自同构群的泛相干态表示分类，揭示了其与Kähler代数结构理论的联系，并提出基于广义Iwasawa分解的方法。
Normalisation holomorphe d'algèbres de type Cartan de champs de vecteurs holomorphes singuliers
本文考虑在公共奇点邻域中的全纯向量场的交换族，例如$0\in \Bbb C^n$。设$\lie g$是维数为$l$的交换复李代数.让$λ_1,...,λ_n\in \lie g^*$和让我们设置$S(g)=\sum_{i=1}^nλ_i(g)x_i\frac{\partial}{\partial x_i}$。我们假设这个李态射是{ \bf丢番图}，在这个意义上，满足一个丢番图条件$(ω(S))$。设$X_1$是$0\in \Bbb C^n$邻域中的全纯向量场.我们假设它的线性部分$s$相对于$S$是正则的，即属于$S(\lie g)$，并且与$S$具有相同的形式中心化子。设$X_2,..., X_l$是与$X_1$交换的在0处消失的全纯向量场.则存在$(\Bbb C^n,0)$的形式同构，使得向量场族在这些形式坐标中为{ \bf范式}。这意味着家庭的每个元素都与$s$交换。证明了：若$X_i$的正规形属于$\hat {\cal O}_n^S\otimes S(\lie g)$（$\hat {\cal O}_n^S$是$S$的形式第一积分环），且其下级部分在$\hat {\cal O}_n^S$上自由，则存在$(\Bbb C^n,0)$的全纯纯同态，它将该族变换为正规形.族中的元素（只有一个）在原点处可能没有非零线性部分。
Rational singularities and quotients by holomorphic group actions
证明了复空间的有理奇点和1-有理奇点在约化和紧李群的全纯作用下是稳定的。这扩展了一个结果的Boutot的分析范畴，并产生一个完善的结果，他的代数范畴。作为主要的技术工具之一，证明了支持在分解纤维上的上同调群的消灭定理。
The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on complex flag supermanifolds, introduced by Yu.I.Manin. We prove that with several exceptions any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebra $\mathfrak {gl}_{m|n}(\mathbb C)$.
Winkelmann considered compact complex manifolds $X$ equipped with a reduced effective normal crossing divisor $D\, \subset\, X$ such that the logarithmic tangent bundle $TX(-\log D)$ is holomorphically trivial. He characterized them as pairs $(X,\, D)$ admitting a holomorphic action of a complex Lie group $\mathbb G$ satisfying certain conditions \cite{Wi1}, \cite{Wi2}; this $\mathbb G$ is the connected component, containing the identity element, of the group of holomorphic automorphisms of $X$ that preserve $D$. We characterize the homogeneous holomorphic principal $H$--bundles over $X$, wher…
The loop space $L\mathbb{P}_1$ of the Riemann sphere consisting of all $C^k$ or Sobolev $W^{k,p}$ maps from the circle $S^1$ to $\mathbb{P}_1$ is an infinite dimensional complex manifold. The loop group $LPGL(2,\mathbb{C})$ acts on $L\mathbb{P}_1$ . We prove that the group of $LPGL(2,\mathbb{C})$ invariant holomorphic line bundles on $L\mathbb{P}_1$ is isomorphic to an infinite dimensional Lie group. Further, we prove that the space of holomorphic sections of these bundles is finite dimensional, and compute the dimension for a generic bundle.
Using mainly tools from [B.13] and [B.15] we give a necessary and sufficient condition in order that a holomorphic action of a connected complex Lie group $G$ on a reduced complex space $X$ admits a strongly quasi-proper meromorphic quotient. We apply this characterization to obtain a result which assert that, when $G = K.B$ \ with $B$ a closed complex subgroup of $G$ and $K$ a real compact subgroup of $G$, the existence of a strongly quasi-proper meromorphic quotient for the $B-$action implies, assuming moreover that there exists a $G-$invariant Zariski open dense subset in $X$ which is good …
Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.
We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebra $\mathfrak{osp}_{2m-1|2n}(\mathbb C)$.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。