Spectral Theory and Almost Periodic Structures in Hom--Lie Banach Algebras
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917105521131520 |
|---|---|
| author | Ennaceur, Marwa |
| author_facet | Ennaceur, Marwa |
| contents | We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $α$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete Bohr--Fourier spectral decomposition of such derivations. We prove that the associated almost periodic and ergodic subspaces are not merely topological complements but closed, $α$-invariant subalgebras, stable under the twisted Lie bracket a key structural novelty that enables coherent restriction of the dynamics. We provide explicit constructions of Hom--Banach--Malcev algebras and demonstrate our theory with concrete operator-algebraic applications, including a novel twisted Weyl algebra example, analyzed via the metaplectic representation, where a non-commuting twist enriches the Bohr spectrum from a cyclic group to a two-dimensional lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Theory and Almost Periodic Structures in Hom--Lie Banach Algebras Ennaceur, Marwa Functional Analysis Rings and Algebras 46H70, 47B47, 43A60, 17D99 J.2; I.1.2 We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $α$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete Bohr--Fourier spectral decomposition of such derivations. We prove that the associated almost periodic and ergodic subspaces are not merely topological complements but closed, $α$-invariant subalgebras, stable under the twisted Lie bracket a key structural novelty that enables coherent restriction of the dynamics. We provide explicit constructions of Hom--Banach--Malcev algebras and demonstrate our theory with concrete operator-algebraic applications, including a novel twisted Weyl algebra example, analyzed via the metaplectic representation, where a non-commuting twist enriches the Bohr spectrum from a cyclic group to a two-dimensional lattice. |
| title | Spectral Theory and Almost Periodic Structures in Hom--Lie Banach Algebras |
| topic | Functional Analysis Rings and Algebras 46H70, 47B47, 43A60, 17D99 J.2; I.1.2 |
| url | https://arxiv.org/abs/2511.21026 |