Root graded groups revisited
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909018336788480 |
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| author | Voronetsky, Egor |
| author_facet | Voronetsky, Egor |
| contents | A group $G$ is called root graded if it has a family of subgroups $G_α$ indexed by roots from a root system $Φ$ satisfying natural conditions similar to Chevalley groups over commutative unital rings. For any such group there is a corresponding algebraic structure (commutative unital ring, associative unital ring, etc.) encoding the commutator relations between $G_α$. We give a complete description of varieties of such structures for irreducible root systems of rank $\geq 3$ excluding $\mathsf H_3$ and $\mathsf H_4$. Moreover, we provide a construction of root graded groups for all algebraic structures from these varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Root graded groups revisited Voronetsky, Egor Group Theory Rings and Algebras 20E42 A group $G$ is called root graded if it has a family of subgroups $G_α$ indexed by roots from a root system $Φ$ satisfying natural conditions similar to Chevalley groups over commutative unital rings. For any such group there is a corresponding algebraic structure (commutative unital ring, associative unital ring, etc.) encoding the commutator relations between $G_α$. We give a complete description of varieties of such structures for irreducible root systems of rank $\geq 3$ excluding $\mathsf H_3$ and $\mathsf H_4$. Moreover, we provide a construction of root graded groups for all algebraic structures from these varieties. |
| title | Root graded groups revisited |
| topic | Group Theory Rings and Algebras 20E42 |
| url | https://arxiv.org/abs/2406.03558 |