scholarly journals Harmonic analysis on the universal covering group of certain semidirect product Lie group

1980 ◽  
Vol 6 (1) ◽  
pp. 129-145
Author(s):  
Takaaki NOMURA
Keyword(s):  
Harmonic Analysis ◽  
Semidirect Product ◽  
Lie Group ◽  
Universal Covering ◽  
Universal Covering Group ◽  
Covering Group

scholarly journals On the fundamental group of a Lie semigroup

1992 ◽  
Vol 34 (3) ◽  
pp. 379-394 ◽  
Author(s):  
Karl-Hermann Neeb
Keyword(s):  
Fundamental Group ◽  
Lie Group ◽  
Unit Group ◽  
Universal Covering ◽  
Covering Group ◽  
Lie Semigroup ◽  
Lie Semigroups ◽  
Inclusion Mapping ◽  
Image Position ◽  
Simply Connected

The simplest type of Lie semigroups are closed convex cones in finite dimensional vector spaces. In general one defines a Lie semigroup to be a closed subsemigroup of a Lie group which is generated by one-parameter semigroups. If W is a closed convex cone in a vector space V, then W is convex and therefore simply connected. A similar statement for Lie semigroups is false in general. There exist generating Lie semigroups in simply connected Lie groups which are not simply connected (Example 1.15). To find criteria for cases when this is true, one has to consider the homomorphisminduced by the inclusion mapping i:S→G, where S is a generating Lie semigroup in the Lie group G. Our main results concern the description of the image and the kernel of this mapping. We show that the image is the fundamental group of the largest covering group of G, into which S lifts, and that the kernel is the fundamental group of the inverse image of 5 in the universal covering group G. To get these results we construct a universal covering semigroup S of S. If j: H(S): = S ∩ S-1 →S is the inclusion mapping of the unit group of S into S, then it turns out that the kernel of the induced mappingmay be identfied with the fundamental group of the unit group H(S)of S and that its image corresponds to the intersection H(S)0 ⋂π1(S), where π1(s) is identified with a central subgroup of S.

Weak amenability of the universal covering group ofSU(1,n)

1990 ◽  
Vol 288 (1) ◽  
pp. 445-472 ◽  
Author(s):  
Mogens Lemvig Hansen
Keyword(s):  
Universal Covering ◽  
Universal Covering Group ◽  
Weak Amenability ◽  
Covering Group
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