Rank-stability of polynomial equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915380927135744 |
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| author | Bauer, Tomer Blachar, Guy Greenfeld, Be'eri |
| author_facet | Bauer, Tomer Blachar, Guy Greenfeld, Be'eri |
| contents | Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of polynomial equations. This leads to a rich theory of stable associative and Lie algebras, with connections to linear soficity, amenability, growth, and group stability. We develop rank-stability and instability tests, examine the effect of algebraic constructions on rank-stability, and prove that while finite-dimensional associative algebras are rank-stable, `most' finite-dimensional Lie algebras are not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rank-stability of polynomial equations Bauer, Tomer Blachar, Guy Greenfeld, Be'eri Rings and Algebras Operator Algebras Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of polynomial equations. This leads to a rich theory of stable associative and Lie algebras, with connections to linear soficity, amenability, growth, and group stability. We develop rank-stability and instability tests, examine the effect of algebraic constructions on rank-stability, and prove that while finite-dimensional associative algebras are rank-stable, `most' finite-dimensional Lie algebras are not. |
| title | Rank-stability of polynomial equations |
| topic | Rings and Algebras Operator Algebras |
| url | https://arxiv.org/abs/2401.04676 |