NORMAL LIE SUBSUPERGROUPS AND NON-ABELIAN SUPERCIRCLES
NORMAL LIE SUBSUPERGROUPS AND NON-ABELIAN SUPERCIRCLES
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正态谎言子超群和非阿贝尔超圆
DOI：
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发表时间：
2002
期刊：
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通讯作者：
T. Stavracou
中科院分区：
文献类型：
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作者：
P. Baguis;T. Stavracou
我们提出并研究了超几何背景下正规李子群的一个适当的类比。证明了李超群与正规李子超群之商所得到的环空间仍然是李超群。我们展示了如何在拓扑非平凡李群上构造李超群结构，以及如何利用正规李子超群的先前性质，以显式地获得这些结构的副积、计数和对映。我们通过在圆上进行先前的构造来说明一般理论，从而导致圆的非阿贝尔超推广。2000数学学科分类：17B70、58A50、58C50。1. 介绍。我们可以将M上所有光滑函数的交换代数C∞(M)与任意可微流形M联系起来，我们可以将C∞(M)作为主要对象，因为微分几何的所有基本概念（切向量、向量束、微分形式等）都涉及与C∞(M)直接相关的结构。在寻求流形概念的推广时，很自然地要去掉C∞(M)的交换性，并考虑对C∞函数的团簇结构进行适当的推广，从而保留了流形M的可微结构的丰富几何内容。特别是[2,3,9,11]的方法，它导致了超流形理论
We propose and study an appropriate analog of normal Lie subgroups in the supergeometrical context. We prove that the ringed space obtained taking the quotient of a Lie supergroup by a normal Lie subsupergroup, is still a Lie supergroup. We show how one can construct Lie supergroup structures over topologically nontrivial Lie groups and how the previous property of normal Lie subsupergroups can be used, in order to explicitly obtain the coproduct, counit, and antipode of these structures. We illustrate the general theory by carrying out the previous constructions over the circle, which leads to non-abelian super generalizations of the circle. 2000 Mathematics Subject Classification: 17B70, 58A50, 58C50. 1. Introduction. We can associate to any differentiable manifold M the commutative algebra C ∞ (M) of all smooth functions on M. Reversing the emphasis, we may regard C ∞ (M) as the primary object, since all of the fundamental concepts of differential geometry (tangent vectors, vector bundles, differential forms, etc.) involve constructions directly related to C ∞ (M). Seeking for generalizations of the notion of manifold, it is natural to remove the commutativity property of C ∞ (M) and consider appropriate generalizations of the sheaf structure of C ∞ -functions, thus preserving a rich geometrical content related to the differentiable structure of the manifold M. In particular, the approach of [2, 3, 9, 11], which led to supermanifold theory, is of