Invariant Projective Properties Under the Action of the Lie Group \(\textrm{SL}(3;\mathbb {R})\) on \(\mathbb{R}\mathbb{P}^2\)

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
Debapriya Biswas, Sandipan Dutta
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引用次数: 0

Abstract

In this paper we define the projective action of the Lie group \(\textrm{SL}(3;\mathbb {R})\) on \(\mathbb{R}\mathbb{P}^2\). We have considered all the one-parameter subgroups (up to conjugacy) of \(\textrm{SL}(3;\mathbb {R})\) and constructed their orbits in two-dimensional homogeneous space by defining the projective action. We obtain the underlying geometry under this action of \(\textrm{SL}(3;\mathbb {R})\) by finding the corresponding invariant projective properties. We also discuss whether the action of \(\textrm{SL}(3;\mathbb {R})\) is triply transitive and to find the possible fixed points under the action.

Abstract Image

李群\(\textrm{SL}(3;\mathbb {R})\)对\(\mathbb{R}\mathbb{P}^2\)作用下的不变射影性质
本文定义了李群\(\textrm{SL}(3;\mathbb {R})\)在\(\mathbb{R}\mathbb{P}^2\)上的投影作用。我们考虑了\(\textrm{SL}(3;\mathbb {R})\)的所有单参数子群(直到共轭),并通过定义射影作用在二维齐次空间中构造了它们的轨道。通过寻找对应的不变射影性质,我们得到了在\(\textrm{SL}(3;\mathbb {R})\)作用下的底层几何。讨论了\(\textrm{SL}(3;\mathbb {R})\)的作用是否具有三传递性,以及在此作用下可能存在的不动点。
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来源期刊
CiteScore
2.60
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology
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