Decomposition and Structure theorems for Garside-like groups with modular lattice structure
| Autor: | Dietzel, Carsten |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Despite being a vast generalization of Garside groups, right $\ell$-groups with noetherian lattice structure and strong order unit share a lot of the properties of Garside groups. In the present work, we prove that every modular noetherian right $\ell$-group with strong order unit decomposes as a direct product of beams, which are sublattices that correspond to the directly indecomposable factors of the strong order interval. Furthermore, we show that the beams of dimension $\delta \geq 4$ can be coordinatized by the $R$-lattices in $Q^{\delta}$, where $Q$ is a noncommutative discrete valuation field with valuation ring $R$. In particular, this gives a precise description of a very big family of modular Garside groups. Comment: 39 pages, Comments welcome! |
| Databáze: | arXiv |
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