Graded Lie algebras of maximal class of type p
| Autor: | Valentina Iusa, Claudio Scarbolo, Sandro Mattarei |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Degree (graph theory) Dimension (graph theory) Field (mathematics) Mathematics - Rings and Algebras Type (model theory) Integer Rings and Algebras (math.RA) 17B70 (Primary) 17B65 17B05 (Secondary) Lie algebra FOS: Mathematics Invariant (mathematics) G110 Pure Mathematics Quotient Mathematics |
| Zdroj: | Journal of Algebra. 588:77-117 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2021.08.013 |
| Popis: | The algebras of the title are infinite-dimensional graded Lie algebras $L= \bigoplus_{i=1}^{\infty}L_i$, over a field of positive characteristic $p$, which are generated by an element of degree $1$ and an element of degree $p$, and satisfy $[L_i,L_1]=L_{i+1}$ for $i\ge p$. %of maximal class in the sense that $L/L^i$ has dimension $i$ for all $i>1$. 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. 40 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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