On a method of determining supports of Thoma's characters of discrete groups
Annales Polonici Mathematici (1997)
- Volume: 67, Issue: 2, page 199-202
- ISSN: 0066-2216
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Abstract
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topErnest Płonka. "On a method of determining supports of Thoma's characters of discrete groups." Annales Polonici Mathematici 67.2 (1997): 199-202. <http://eudml.org/doc/270725>.
@article{ErnestPłonka1997,
abstract = {We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.},
author = {Ernest Płonka},
journal = {Annales Polonici Mathematici},
keywords = {positive definite functions; characters; traces; positive definite function; GNS-representation; -algebra; nilpotent groups; von Neumann algebras},
language = {eng},
number = {2},
pages = {199-202},
title = {On a method of determining supports of Thoma's characters of discrete groups},
url = {http://eudml.org/doc/270725},
volume = {67},
year = {1997},
}
TY - JOUR
AU - Ernest Płonka
TI - On a method of determining supports of Thoma's characters of discrete groups
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 199
EP - 202
AB - We present a new approach to determining supports of extreme, normed by 1, positive definite class functions of discrete groups, i.e. characters in the sense of E. Thoma [8]. Any character of a group produces a unitary representation and thus a von Neumann algebra of linear operators with finite normal trace. We use a theorem of H. Umegaki [9] on the uniqueness of conditional expectation in finite von Neumann algebras. Some applications and examples are given.
LA - eng
KW - positive definite functions; characters; traces; positive definite function; GNS-representation; -algebra; nilpotent groups; von Neumann algebras
UR - http://eudml.org/doc/270725
ER -
References
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- [3] M. Hall, The Theory of Groups, New York, Macmillan, 1969.
- [4] R. E. Howe, On representation of finitely generated discrete torsion free nilpotent groups, Pacific J. Math. 73 (1977), 281-305. Zbl0387.22005
- [5] E. Kaniuth und R. Lasser, Zum verallgemeinerten Wienerschen Satz über diskrete nilpotente Gruppen der Klasse 3, Math. Z. 163 (1978), 39-55.
- [6] E. Płonka, Remarks on characters of discrete nilpotent groups, Math. Ann. 240 (1979), 97-102. Zbl0405.43004
- [7] S. Sakai, C*-algebras and W*-algebras, Springer, 1971.
- [8] E. Thoma, Über unitäre Darstellungen abzählbarer Gruppen, Math. Ann. 153 (1964), 111-139. Zbl0136.11603
- [9] H. Umegaki, Condional expectation in operator algebras, Tôhoku Math. J. 6 (1954), 1977-1981.
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