实流形、复流形和四元数流形的环群和环同态群的半直积
Semidirect products of groups of loops and groups of diffeomorphisms of real, complex and quaternion manifolds
摘要：
本文主要研究有限维和无穷维实流形、复流形和四元数流形的环群和环同态群的半直积。证明了地图集图间具有四元数全纯转移映射的四元数流形的必要性。借助于群$G$相对于稠密子群$G'$的随机过程和拟不变转移测度，构造了这些群的酉表示，包括不可约群.证明了该过程提供了一个两两非等价不可约酉表示的基数$card ({\bf R})$族。研究了这种表示的可微性。
英文摘要：
This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds with quaternion holomorphic transition mappings between charts of atlases are proved. Unitary representations of these groups including irreducible are constructed with the help of stochastic processes and quasi-invariant transition measures on groups $G$ relative to dense subgroups $G'$. It is proved, that this procedure provides a family of the cardinality $card ({\bf R})$ of pairwise nonequivalent irreducible unitary representations. A differentiability of such representations is studied.
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