Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000567660> ?p ?o ?g. }
Showing items 1 to 54 of
54
with 100 items per page.
- W2000567660 endingPage "822" @default.
- W2000567660 startingPage "822" @default.
- W2000567660 abstract "At present, little general information seems to be available concerning the fixed points of compact abelian groups operating on Euclidean n dimensional space, En. In view of this fact, it is perhaps worthwhile to enlarge our information concerning special cases of such phenomena. One such special case, is the classical theorem that a compact abelian group of affine transformations has a fixed point. It is our intention to generalize this theorem to connected simply connected, nilpotent Lie groups. In order to see clearly the nature of the generalization, we shall first present a description of the affine groups, A (n) and its action on En. Let El be considered as a vector space or abelian Lie group. Then GL(n, R) is the group of continuous automorphisms of En and A (n) is the semi-direct product of En and GL(n, R). Ve will denote this by A (n) = En GL(n, R) and an element of A (n) will be denoted by (r, g) where rEEn and gEGL(n, R). Then multiplication in A(n) is defined by (r1, gl) (r2, g2)= (rig,(r2), glg2) . We can also define a mapping -q: A(n)->El by tq(r, g) =r. Then the action of A(n) on En is given by r-*i-(aor) for all rCEEn and aoEA (n). Now let Nn be a connected, simply connected n dimensional nilpotent Lie group. Then Nn is homeomorphic to En. Let G(Nn) be the group of continuous automorphisms of Nn and define the group A (Nn) as the semi-direct product of Nn and G(Nn). Then A (Nn) = NnG(Nn) and the elements of A (Nn) will be denoted by (n, g) for n -Nn and g G(Nn). Then multiplication in A (Nn) is given by (nl, gl) (n2, g2) = (nlgl(n2), g1g2). We can clearly define A (Nn) operating on Nn exactly as in the abelian case of En." @default.
- W2000567660 created "2016-06-24" @default.
- W2000567660 creator A5048231405 @default.
- W2000567660 date "1958-05-01" @default.
- W2000567660 modified "2023-10-14" @default.
- W2000567660 title "A fixed point theorem for nilpotent Lie groups" @default.
- W2000567660 cites W2082717048 @default.
- W2000567660 cites W2329673299 @default.
- W2000567660 doi "https://doi.org/10.1090/s0002-9939-1958-0095896-5" @default.
- W2000567660 hasPublicationYear "1958" @default.
- W2000567660 type Work @default.
- W2000567660 sameAs 2000567660 @default.
- W2000567660 citedByCount "4" @default.
- W2000567660 countsByYear W20005676602016 @default.
- W2000567660 crossrefType "journal-article" @default.
- W2000567660 hasAuthorship W2000567660A5048231405 @default.
- W2000567660 hasBestOaLocation W20005676601 @default.
- W2000567660 hasConcept C187915474 @default.
- W2000567660 hasConcept C202444582 @default.
- W2000567660 hasConcept C206219070 @default.
- W2000567660 hasConcept C2524010 @default.
- W2000567660 hasConcept C28719098 @default.
- W2000567660 hasConcept C33923547 @default.
- W2000567660 hasConcept C45962547 @default.
- W2000567660 hasConcept C50555996 @default.
- W2000567660 hasConceptScore W2000567660C187915474 @default.
- W2000567660 hasConceptScore W2000567660C202444582 @default.
- W2000567660 hasConceptScore W2000567660C206219070 @default.
- W2000567660 hasConceptScore W2000567660C2524010 @default.
- W2000567660 hasConceptScore W2000567660C28719098 @default.
- W2000567660 hasConceptScore W2000567660C33923547 @default.
- W2000567660 hasConceptScore W2000567660C45962547 @default.
- W2000567660 hasConceptScore W2000567660C50555996 @default.
- W2000567660 hasIssue "5" @default.
- W2000567660 hasLocation W20005676601 @default.
- W2000567660 hasOpenAccess W2000567660 @default.
- W2000567660 hasPrimaryLocation W20005676601 @default.
- W2000567660 hasRelatedWork W1978898788 @default.
- W2000567660 hasRelatedWork W2023736675 @default.
- W2000567660 hasRelatedWork W2215319315 @default.
- W2000567660 hasRelatedWork W2273568450 @default.
- W2000567660 hasRelatedWork W2963450278 @default.
- W2000567660 hasRelatedWork W3011491025 @default.
- W2000567660 hasRelatedWork W3012218436 @default.
- W2000567660 hasRelatedWork W3174904736 @default.
- W2000567660 hasRelatedWork W4242595863 @default.
- W2000567660 hasRelatedWork W4248510752 @default.
- W2000567660 hasVolume "9" @default.
- W2000567660 isParatext "false" @default.
- W2000567660 isRetracted "false" @default.
- W2000567660 magId "2000567660" @default.
- W2000567660 workType "article" @default.