A Lie algebra for Fr?licher groups

详细信息    查看全文

• 作者：Martin  ; Laubinger  ; ;   ; ^a ;   ; ^{mlaubing@math.upb.de}
• 刊名：Indagationes Mathematicae
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：21
• 期：3-4
• 页码：156-174
• 全文大小：257 K

文摘

Fr?licher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as or , and also projective limits of Lie groups, are in a natural way objects of that category, and group operations are morphisms in the category. We call groups with this property Fr?licher groups. One can define tangent spaces to Fr?licher spaces, and in the present article we prove that, under a certain additional assumption, the tangent space at the identity of a Fr?licher group can be equipped with a Lie bracket. We discuss an example which satisfies the additional assumption.