Length functions exponentially distorted on subgroups of complex Lie groups
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917792802930688 |
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| author | Aristov, Oleg |
| author_facet | Aristov, Oleg |
| contents | We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie group there is a maximum equivalence class of length functions exponentially distorted on a normal integral subgroup lying between the exponential and nilpotent radicals. Moreover, a function in this class admits an asymptotic decomposition similar to that previously found by the author for word length functions, i.e., in the case of exponential radical [J. Lie Theory 29:4, 1045--1070, 2019]. In the general case we use auxiliary length functions constructed via holomorphic homomorphisms to Banach PI-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12667 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Length functions exponentially distorted on subgroups of complex Lie groups Aristov, Oleg Functional Analysis We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie group there is a maximum equivalence class of length functions exponentially distorted on a normal integral subgroup lying between the exponential and nilpotent radicals. Moreover, a function in this class admits an asymptotic decomposition similar to that previously found by the author for word length functions, i.e., in the case of exponential radical [J. Lie Theory 29:4, 1045--1070, 2019]. In the general case we use auxiliary length functions constructed via holomorphic homomorphisms to Banach PI-algebras. |
| title | Length functions exponentially distorted on subgroups of complex Lie groups |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2208.12667 |