Geodesic
Simplicite des Groupes Unitaires Definis par un Facteur Simple
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 87-95

Voir la notice de l'article provenant de la source Cambridge University Press

Let B be a σ-finite von Neumann factor of type II1 or III and let σ be an involutory *-antiautomorphism of B. We consider U(B) the unitary group of B and its subgroup G = {g ∈U(B) | σ(g) = g*}, which are unitary classical groups. In this paper, we prove that G has a unique non trivial normal subgroup, which is its centre {±1}.
DOI : 10.4153/CMB-1984-013-6
Mots-clés : 46410 
Giordano, Thierry; Harpe, Pierre De La. Simplicite des Groupes Unitaires Definis par un Facteur Simple. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 87-95. doi: 10.4153/CMB-1984-013-6
@article{10_4153_CMB_1984_013_6,
     author = {Giordano, Thierry and Harpe, Pierre De La},
     title = {Simplicite des {Groupes} {Unitaires} {Definis} par un {Facteur} {Simple}},
     journal = {Canadian mathematical bulletin},
     pages = {87--95},
     year = {1984},
     volume = {27},
     number = {1},
     doi = {10.4153/CMB-1984-013-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-013-6/}
}
TY  - JOUR
AU  - Giordano, Thierry
AU  - Harpe, Pierre De La
TI  - Simplicite des Groupes Unitaires Definis par un Facteur Simple
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 87
EP  - 95
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-013-6/
DO  - 10.4153/CMB-1984-013-6
ID  - 10_4153_CMB_1984_013_6
ER  - 
%0 Journal Article
%A Giordano, Thierry
%A Harpe, Pierre De La
%T Simplicite des Groupes Unitaires Definis par un Facteur Simple
%J Canadian mathematical bulletin
%D 1984
%P 87-95
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-013-6/
%R 10.4153/CMB-1984-013-6
%F 10_4153_CMB_1984_013_6

[1] 1. Bonsall, F. F. et Duncan, J., Complete normed algebras, Springer-Verlag, New York-Berlin- Heidelberg 1973. Google Scholar

[2] 2. Douglas, R. G., Banach algebra techniques in operator theory, Academic Press, New York 1972. Google Scholar

[3] 3. Dye, H. A., On the geometry of projections in certain operator algebras, Ann. of Math. 61 (1955) 73-89. Google Scholar

[4] 4. Giordano, T., Antiautomorphismes involutifs des facteurs de von Neumann injectifs, thèse, Neuchâtel, 1981; voir aussi C. R. Acad. Sci. Paris, Sér. A, 291 (1980) 583-585. Google Scholar

[5] 5. de la Harpe, P., Simplicity of the projective unitary groups defined by simple factors, Comment. Math. Helv. 54 (1979) 334-345. Google Scholar

[6] 6. de la Harpe, P., Classical groups and classical Lie algebras of operators, Operator Algebras and Applications. Proc. in Pure Math., Amer. Math. Soc. Vol. 38, part. I, pages 477-513. Google Scholar

[7] 7. Størmer, E., On anti-automorphisms of von Neumann algebras, Pacific J. Math. 21 (1967) 349-370. Google Scholar

[8] 8. Stratila, S. et Zsido, L., Lectures on von Neumann algebras, Abacus Press, Kent 1979. Google Scholar

[9] 9. Topping, D. M., Jordan algebras of self-adjoint operators, Mem. Amer. Math. Soc. 53, A.M.S. Providence R. I. 1965. Google Scholar

[10] 10. Upmeier, H., Automorphism groups of Jordan C*-algebras, Math. Z. 176 (1981) 21-34. Google Scholar

Cité par Sources :