S^3上当前群的扩张及其伴随表示
Extensions of Current Groups on S^3 and the Adjoint Representations
摘要：
设Ω ^3（SU（n））是从S^3到SU（n）的基映射的李群.利用S^3上SU（n）-联络的仿射对偶空间的阿贝尔群构造了Ω ^3（SU（n））的李群扩张（n>2）。本文改进了J. Mickelsson在1987年的结果，特别是对非单位连通区的扩张给出了精确的描述.我们还纠正了米克尔森关于Ω ^3（SU（2））的延拓的几个论点，虽然他关于Ω ^3（SU（2））的延拓约化为Z_2的延拓的观察是正确的。然后我们将研究n>2时Ω ^3（SU（n））的李群扩张的伴随表示。
英文摘要：
Let Omega^3(SU(n)) be the Lie group of based mappings from S^3 to SU(n). We construct a Lie group extension of Omega^3(SU(n)) for n>2 by the abelian group of the affine dual space of SU(n)-connections on S^3. In this article we give several improvement of J. Mickelsson's results in 1987, especially we give a precise description of the extension of those components that are not the identity component,. We also correct several argument about the extension of Omega^3(SU(2)) which seems not to be exact in Mickelsson's work, though his observation about the fact that the extension of Omega^3(SU(2)) reduces to the extension by Z_2 is correct. Then we shall investigate the adjoint representation of the Lie group extension of Omega^3(SU(n)) for n>2.
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