{"product_id":"cohomological-aspects-of-complete-reducibility-of-representations-von-ioannis-farmakis","title":"COHOMOLOGICAL ASPECTS OF COMPLETE REDUCIBILITY OF REPRESENTATIONS","description":"\u003cp\u003eIn this thesis we deal with questions of continuous group cohomology of continuous representations of a separable locally compact group on a real or complex Banach space. Of particular importance is the case of a compact group. Here we use äne actions to prove vanishing theorems. To do this, we give an alternative de¿nition of the cohomology, which is recursive. As a consequence we prove under certain conditions (equivalent with the existence of a non-trivial simultaneous ¿xed point of the associated äne map) all cohomology groups vanish. When G is a connected Lie group, we study the relationship of its cohomology with the corresponding Lie algebra cohomology. Finally, we consider the situation of a closed subgroup H of G which is cocompact and of co¿nite volume and show just as in the case of a compact group that the restriction map H^n(G,V)--\u0026gt;H^n(H,V) is injective and apply this to questions of complete reducibility of representations.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783843377775\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783843377775","offer_id":39470113357917,"sku":"9783843377775","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/94901d4b-3c98-42dc-a0a9-816b4df9e8d5.jpg?v=1759119998","url":"https:\/\/shop.autorenwelt.de\/products\/cohomological-aspects-of-complete-reducibility-of-representations-von-ioannis-farmakis","provider":"Autorenwelt Shop","version":"1.0","type":"link"}