A direct proof of Leutbecher's Lemma
Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 179-180
Voir la notice de l'article provenant de la source Cambridge University Press
Using the theory of group extensions, A. Leutbecher [1] proved thisLemma. Let G bea group, and w some 2-cocycle of a trivial G-module M. The cohomology class ofw will contain symmetric cocycles if and only if w is semisymmetric.Here we have called w symmetric or semisymmetric according as w(h, g) = w(g, h) for all g, h ∈G or only for those with hg = gh. In one direction, the proof reduces to observing that 2-coboundaries of trivial G-modules are semisymmetric. The nontrivial part of the lemma also admits of a straightforward proof, as follows.
Wohlfahrt, Klaus. A direct proof of Leutbecher's Lemma. Glasgow mathematical journal, Tome 13 (1972) no. 2, pp. 179-180. doi: 10.1017/S0017089500001634
@article{10_1017_S0017089500001634,
author = {Wohlfahrt, Klaus},
title = {A direct proof of {Leutbecher's} {Lemma}},
journal = {Glasgow mathematical journal},
pages = {179--180},
year = {1972},
volume = {13},
number = {2},
doi = {10.1017/S0017089500001634},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001634/}
}
[1] 1.Leutbecher, A., Über Automorphiefaktoren und die Dedekindschen Summen, Glasgow Math. J. 11 (1970), 41–57. Google Scholar | DOI
[2] 2.Petersson, H., Zur analytischen Theorie der Grenzkreisgruppen, Teil I, Math. Ann. 115 (1937), 23–67. Google Scholar | DOI
Cité par Sources :