关于某些幺半群作用的注记
A note on actions of some monoids
摘要：
实数的乘法幺半群$(\mathbb{R},\cdot)$在流形上的光滑作用导致了另一种，并且由于某些原因更简单，向量丛，双重向量丛和相关结构如分次丛的定义[Grabowski和Rotkiewicz，J. Geom. Phys. 2011]。由于这些原因，研究某些与幺半群$(\mathbb{R},\cdot)$密切相关的幺半群的光滑作用是很自然的。也就是说，我们讨论了与以下几个方面有关的几何结构：乘性复数幺半群的光滑作用和全纯作用，穿孔映射$(\mathbb{R},0)\rightarrow (\mathbb{R},0)$的第二喷流幺半群的光滑作用，实2 × 2矩阵幺半群的光滑作用以及乘性实在超流形上的光滑作用.在特殊情况下，我们恢复的概念的全纯向量丛，一个复杂的向量丛和非负分次流形。
英文摘要：
Smooth actions of the multiplicative monoid $(\mathbb{R},\cdot)$ of real numbers on manifolds lead to an alternative, and for some reasons simpler, definition of a vector bundle, a double vector bundle and related structures like a graded bundle [Grabowski and Rotkiewicz, J. Geom. Phys. 2011]. For these reasons it is natural to study smooth actions of certain monoids closely related with the monoid $(\mathbb{R},\cdot)$ . Namely, we discuss geometric structures naturally related with: smooth and holomorphic actions of the monoid of multiplicative complex numbers, smooth actions of the monoid of second jets of punctured maps $(\mathbb{R},0)\rightarrow (\mathbb{R},0)$, smooth action of the monoid of real 2 by 2 matrices and smooth actions of multiplicative reals on a supermanifold. In particular cases we recover the notions of a holomorphic vector bundle, a complex vector bundle and a non-negatively graded manifold.
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