# 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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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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- [2] A. L. Carey and W. Moran, Characters of nilpotent groups, Math. Proc. Cambridge Philos. Soc. 96 (1984), 123-137. Zbl0549.43004
- [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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