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arXiv · 2506.11819

Prime and semiprime Lie ideals in C*-algebras

Eusebio Gardella·Kan Kitamura·Hannes Thiel
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Abstract

Using the theory of Dixmier ideals developed in previous work, we show that every semiprime Lie ideal in a C*-algebra arises as the full normalizer subspace of a semiprime two-sided ideal. This leads to a concise description of all semiprime Lie ideals in terms of semiprime two-sided ideals, and an analogous description of prime Lie ideals in terms of prime two-sided ideals. For unital C*-algebras without characters, we obtain a natural bijection between (semi)prime two-sided ideals and (semi)prime Lie ideals, and it follows that a Lie ideal is fully noncentral if and only if it is not contained in any prime Lie ideal.

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Eusebio Gardella, Kan Kitamura, Hannes Thiel. 2026-09-06. Prime and semiprime Lie ideals in C*-algebras. https://arxiv.org/abs/2506.11819

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