Symmetry and nonsymmetry for locally compact groups

Leptin, Horst; Poguntke, Detlev

doi:10.1016/0022-1236(79)90107-1

Cited by 43 publications

(52 citation statements)

References 12 publications

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“…It follows from the work of Losert [Lo] that a discrete group satisfies (W ) if and only if it is "symmetric". Finitely generated virtually nilpotent discrete groups are symmetric by [LeP,Corollary 3].…”

Section: Proof Assume That γ Satisfies (W ) and Considermentioning

confidence: 99%

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

Deninger¹

2006

J. Amer. Math. Soc.

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In 1990, Lind, Schmidt, and Ward gave a formula for the entropy of certain Z n \mathbb {Z}^n -dynamical systems attached to Laurent polynomials P P , in terms of the (logarithmic) Mahler measure of P P . We extend the expansive case of their result to the noncommutative setting where Z n \mathbb {Z}^n gets replaced by suitable discrete amenable groups. Generalizing the Mahler measure, Fuglede–Kadison determinants from the theory of group von Neumann algebras appear in the entropy formula.

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Section: Proof Assume That γ Satisfies (W ) and Considermentioning

confidence: 99%

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

Deninger¹

2006

J. Amer. Math. Soc.

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“…Symmetry in group algebras has been investigated by various authors (see, for instance, [17,19]). One can easily verify that a Banach [11] Ideals in operator space projective tensor products 285 is nontrivial, where B α (v, w) := B(vα, wα) for all v, w ∈ A (see [19]).…”

Section: The Wiener Property and Symmetrymentioning

confidence: 99%

IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C^*-ALGEBRAS

Jain¹,

Kumar²

2011

J. Aust. Math. Soc.

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Let A and B be C * -algebras. We prove the slice map conjecture for ideals in the operator space projective tensor product A ⊗ B. As an application, a characterization of the prime ideals in the Banach * -algebra A ⊗ B is obtained. In addition, we study the primitive ideals, modular ideals and the maximal modular ideals of A ⊗ B. We also show that the Banach * -algebra A ⊗ B possesses the Wiener property and that, for a subhomogeneous C * -algebra A, the Banach * -algebra A ⊗ B is symmetric.2010 Mathematics subject classification: primary 46L06; secondary 46L07, 47L25.

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“…I will shortly introduce the concept of symmetry and explain the relation to finite rank operators. In fact, I got interested in the existence of finite rank operators by asking for the symmetry of group algebras of exponential Lie 0025-5831/82/0259/0371/$02.60 groups, and in some sense the present article may be considered as an appendix or continuation of my paper [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Theorem Let G Be An Exponential Lie Group and Let ~ Be An Imentioning

confidence: 99%

“…The set G of equivalence classes of irreducible unitary representations of the exponential Lie group G is in a canonical bijective correspondence with the set of G-orbits (under the coadjoint action) in g*, the real dual of the Lie algebra g of G, see e.g. [12]. In the sequel, I will describe (and use) a somewhat unusual procedure to obtain all the irreducible unitary representations of G.…”

Section: U* L I(x1 Li(x2) T)*u =Teumentioning

confidence: 99%

Operators of finite rank in unitary representations of exponential Lie groups

Poguntke

1982

Math. Ann.

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Symmetry and nonsymmetry for locally compact groups

Cited by 43 publications

References 12 publications

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C^*-ALGEBRAS

Operators of finite rank in unitary representations of exponential Lie groups

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Symmetry and nonsymmetry for locally compact groups

Cited by 43 publications

References 12 publications

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C*-ALGEBRAS

Operators of finite rank in unitary representations of exponential Lie groups

Contact Info

Product

Resources

About

IDEALS IN OPERATOR SPACE PROJECTIVE TENSOR PRODUCT OF C^*-ALGEBRAS