Varieties of a class of elementary subalgebras
| Autor: | Yang Pan, Yanyong Hong |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Physics
General Mathematics Dimension (graph theory) Subalgebra elementary subalgebras commuting roots Type (model theory) Combinatorics Restricted Lie algebra Algebraic group Lie algebra QA1-939 Variety (universal algebra) Algebraically closed field Mathematics::Representation Theory irreducible components Mathematics |
| Zdroj: | AIMS Mathematics, Vol 7, Iss 2, Pp 2084-2101 (2022) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2022119?viewType=HTML |
| Popis: | Let $ G $ be a connected standard simple algebraic group of type $ C $ or $ D $ over an algebraically closed field $ \Bbbk $ of positive characteristic $ p > 0 $, and $ \mathfrak{g}: = \mathrm{Lie}(G) $ be the Lie algebra of $ G $. Motivated by the variety of $ \mathbb{E}(r, \mathfrak{g}) $ of $ r $-dimensional elementary subalgebras of a restricted Lie algebra $ \mathfrak{g} $, in this paper we characterize the irreducible components of $ \mathbb{E}(\mathrm{rk}_{p}(\mathfrak{g})-1, \mathfrak{g}) $ where the $ p $-rank $ \mathrm{rk}_{p}(\mathfrak{g}) $ is defined to be the maximal dimension of an elementary subalgebra of $ \mathfrak{g} $. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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