On a method of determining supports of Thoma's characters of discrete groups

• Autorzy: Ernest Płonka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

positive definite functions; characters; traces

Kategorie tematyczne

• 43A40: Character groups and dual objects
• 43A35: Positive definite functions on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1997
• Tom: 67
• Numer: 2
• Strony: 199-202

Daty

wydano

1997

otrzymano

1996-09-20

poprawiono

1996-11-05

Twórcy

autor

Ernest Płonka

• Institute of Mathematics Silesian, Technical University, Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] R. J. Blattner, On induced representations, Amer. J. Math. 83 (1961), 79-98.
• [2] A. L. Carey and W. Moran, Characters of nilpotent groups, Math. Proc. Cambridge Philos. Soc. 96 (1984), 123-137.
• [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.
• [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.
• [7] S. Sakai, C*-algebras and W*-algebras, Springer, 1971.
• [8] E. Thoma, Über unitäre Darstellungen abzählbarer Gruppen, Math. Ann. 153 (1964), 111-139.
• [9] H. Umegaki, Condional expectation in operator algebras, Tôhoku Math. J. 6 (1954), 1977-1981.