By Joachim Erven

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Then the closure of V is . F r o m this t h e o r e m it is clear w h a t we are g o i n g to do now. 3)). by ]]k(8)v = elngv is called the n-th eigenspace Hn SU(I,I) 'V %6 ]R } of Hn'S K in ~ . w h i c h can all be found in S. 1)). 3) (iv) we a l r e a d y Thus w e only have on 67 H n , which venient of dH(A) know to study together therefore the action the a c t i o n with to take for the e i g e n v a l u e A of dH(A) in on such an of the two o t h e r form a basis o % ~ the c o m p l e x i f i c a t i o n % .

Described [22]). 2) other are the cocycles Maurer-Cartan-cocy- so-called do n o t exist for the Euclidean Groups. The Cohomology of the First Leibniz-Extension of C o m p a c t Lie- Groups In [22] the Leibnitz-Extension was tain factorizable representations. pute the relevant cohomology with Lie Algebra The crucial [14] p. 71). point Thus ~ Q is . We It is groups. consider that again defined GL the So GL in o r d e r thus G (cf. ). is a r e g u l a r theory of of let to d e t e r m i n e some be interest a compact semi-direct section to c o m - Lie product I is a p p l i c a b l e cer- group (cf.

From cE ~ equivalence Schur's . d. Remark: The cocycles oles (cf. Motion 3. described [22]). 2) other are the cocycles Maurer-Cartan-cocy- so-called do n o t exist for the Euclidean Groups. The Cohomology of the First Leibniz-Extension of C o m p a c t Lie- Groups In [22] the Leibnitz-Extension was tain factorizable representations. pute the relevant cohomology with Lie Algebra The crucial [14] p. 71). point Thus ~ Q is . We It is groups. consider that again defined GL the So GL in o r d e r thus G (cf.