单环变形q-映射空间的对称性

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-10-03 DOI:10.1007/s00220-025-05433-z

Vicente Cortés, Alejandro Gil-García, Danu Thung

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引用次数: 0

摘要

q -映射空间形成了一类重要的负标量曲率四元数Kähler流形。它们的单环变形总是非齐次的，并被用来构造同齐次一四元数Kähler流形作为齐次空间的变形。这里我们研究变形情况下的等距群。我们的主要结论是：对于4n维的q映射空间，它总是包含\(\mathbb {R}^{n-1}\)的一组仿射变换与\(2n+1\)维的Heisenberg群的半直积。仿射群及其对半直积中正规海森堡因子的作用依赖于编码q映射空间的三次仿射超曲面。

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Symmetries of One-loop Deformed q-map Spaces

Q-map spaces form an important class of quaternionic Kähler manifolds of negative scalar curvature. Their one-loop deformations are always inhomogeneous and have been used to construct cohomogeneity one quaternionic Kähler manifolds as deformations of homogeneous spaces. Here we study the group of isometries in the deformed case. Our main result is the statement that it always contains a semidirect product of a group of affine transformations of \(\mathbb {R}^{n-1}\) with a Heisenberg group of dimension \(2n+1\) for a q-map space of dimension 4n. The affine group and its action on the normal Heisenberg factor in the semidirect product depend on the cubic affine hypersurface which encodes the q-map space.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.