Simplicity, bounded normal generation, and automatic continuity of groups of unitaries

Chand, Abhinav; Robert, Leonel

doi:10.1016/j.aim.2023.108894

Advances in Mathematics

2023

DOI: 10.1016/j.aim.2023.108894

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Simplicity, bounded normal generation, and automatic continuity of groups of unitaries

Abhinav Chand

Leonel Robert

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Cited by 4 publications

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Nowhere scattered multiplier algebras

Vilalta

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We study sufficient conditions under which a nowhere scattered $\mathrm {C}^*$ -algebra $A$ has a nowhere scattered multiplier algebra $\mathcal {M}(A)$ , that is, we study when $\mathcal {M}(A)$ has no nonzero, elementary ideal-quotients. In particular, we prove that a $\sigma$ -unital $\mathrm {C}^*$ -algebra $A$ of (i) finite nuclear dimension, or (ii) real rank zero, or (iii) stable rank one with $k$ -comparison, is nowhere scattered if and only if $\mathcal {M}(A)$ is.

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Nowhere scattered multiplier algebras

Vilalta

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Unitary groups, $\boldsymbol{K}$ -theory, and traces

Sarkowicz

2023

Glasgow Math. J.

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We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$ -theoretic regularity conditions, these maps can be seen to commute with the pairing between $K_0$ and traces. If the homomorphism is contractive and sends the unit circle to the unit circle, the map between spaces of continuous real-valued affine functions can further be shown to be unital and positive (up to a minus sign).

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Distinguishing C*-algebras by their unitary groups

Fogang Takoutsing,

Robert

2024

Proc. Amer. Math. Soc.

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Simplicity, bounded normal generation, and automatic continuity of groups of unitaries

Cited by 4 publications

References 44 publications

Nowhere scattered multiplier algebras

Nowhere scattered multiplier algebras

Unitary groups, $\boldsymbol{K}$ -theory, and traces

Distinguishing C*-algebras by their unitary groups

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