Discrete nilpotent groups have a $T_{1}$ primitive ideal space

Poguntke, Detlev

doi:10.4064/sm-71-3-271-275

Cited by 11 publications

(10 citation statements)

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“…To illustrate this we shall prove a structure theorem for the set of characters of G in terms of the (abelian) quotient groups in a central series. Though a similar result would follow from a result of Poguntke [13] our proof of this result is simpler and sharper.…”

Section: Introductionsupporting

confidence: 74%

Characters of nilpotent groups

Carey

Moran

1984

Math. Proc. Camb. Phil. Soc.

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The characters (extremal positive definite central functions) of discrete nilpotent groups are studied. The relationship between the set of characters of G and the primitive ideals of the group C*-algebra C*(G) is investigated. It is shown that for a large class of nilpotent groups these objects are in 1–1 correspondence. One proof of this exploits the fact that faithful characters of certain nilpotent groups vanish off the finite conjugacy class subgroup. An example is given where the latter property fails.

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Section: Introductionsupporting

confidence: 74%

Characters of nilpotent groups

Carey

Moran

1984

Math. Proc. Camb. Phil. Soc.

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“…(See the considerations in the last part of [9] and [7].) The following (probably) wellknown lemma will be used several times.…”

Section: Introductionmentioning

confidence: 99%

Prime ideals in the C*-algebra of a nilpotent group

Ludwig

1986

Monatshefte f�r Mathematik

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“…Among finitely generated groups, the virtually nilpotent ones (Definition 2.1) turn out to be precisely those groups whose irreducible representations always generate simple nuclear C*-algebras [24,27,34]. Therefore irreducible representations of virtually nilpotent groups form the largest class of groups (and representations) to which one may hope to apply the results of the Elliott classification program.…”

Section: Introductionmentioning

confidence: 99%

Finite decomposition rank for virtually nilpotent groups

Eckhardt

Gillaspy

McKenney

2018

Trans. Amer. Math. Soc.

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We show that inductive limits of virtually nilpotent groups have strongly quasidiagonal C*-algebras, extending results of the first author on solvable virtually nilpotent groups. We use this result to show that the decomposition rank of the group C*-algebra of a finitely generated virtually nilpotent group G is bounded by 2 · h(G)! − 1, where h(G) is the Hirsch length of G. This extends and sharpens results of the first and third authors on finitely generated nilpotent groups. It then follows that if a C*-algebra generated by an irreducible representation of a virtually nilpotent group satisfies the universal coefficient theorem, it is classified by its Elliott invariant.

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Discrete nilpotent groups have a $T_{1}$ primitive ideal space

Cited by 11 publications

References 0 publications

Characters of nilpotent groups

Characters of nilpotent groups

Prime ideals in the C*-algebra of a nilpotent group

Finite decomposition rank for virtually nilpotent groups

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