Graded Lie algebras of maximal class of type $p$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909467191279616 |
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| author | Iusa, Valentina Mattarei, Sandro Scarbolo, Claudio |
| author_facet | Iusa, Valentina Mattarei, Sandro Scarbolo, Claudio |
| contents | The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, that are generated by an element of degree $1$ and an element of degree $p$, and satisfy $[L_i,L_1]=L_{i+1}$ for $i\ge p$. In case $p=2$ such algebras were classified by Caranti and Vaughan-Lee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_08354 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Graded Lie algebras of maximal class of type $p$ Iusa, Valentina Mattarei, Sandro Scarbolo, Claudio Rings and Algebras 17B70 (Primary) 17B65, 17B05 (Secondary) The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, that are generated by an element of degree $1$ and an element of degree $p$, and satisfy $[L_i,L_1]=L_{i+1}$ for $i\ge p$. In case $p=2$ such algebras were classified by Caranti and Vaughan-Lee in 2003. We announce an extension of that classification to arbitrary prime characteristic, and prove several major steps in its proof. |
| title | Graded Lie algebras of maximal class of type $p$ |
| topic | Rings and Algebras 17B70 (Primary) 17B65, 17B05 (Secondary) |
| url | https://arxiv.org/abs/2011.08354 |