C*-模的射影空间
Projective space of a C*-module
摘要：
设X是A上的右Hilbert C*-模。研究了X的射影空间P（X）的几何和拓扑，P（X）由X的正交可补子模构成，这些子模由单个元素生成.我们还研究了p球S_p（X）和自然纤维化S_p（X）\to P（X）的几何，其中S_p（X）={x \in X：<x，x>=p}，p在A中为投影.证明了射影空间和p-球面是X的伴随算子代数L_A（X）的酉群的齐次可微空间。这些空间的同伦理论进行检查。
英文摘要：
Let X be a right Hilbert C*-module over A. We study the geometry and the topology of the projective space P(X) of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also study the geometry of the p-sphere S_p(X) and the natural fibration S_p(X) \to P(X), where S_p(X)={x\in X: <x,x>=p}, for p in A a projection. The projective space and the p-sphere are shown to be homogeneous differentiable spaces of the unitary group of the algebra L_A(X) of adjointable operators of X. The homotopy theory of these spaces is examined.
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。
