Fine Gradings on the exceptional Lie algebra $\mathfrak d_4$
| dc.creator | Draper, Cristina | |
| dc.creator | Martín, Cándido | |
| dc.creator | Viruel, Antonio | |
| dc.date | 2008-04-10 | |
| dc.date.accessioned | 2026-07-07T09:31:36Z | |
| dc.date.available | 2026-07-07T09:31:36Z | |
| dc.description | We describe all the fine group gradings, up to equivalence, on the Lie algebra $\mathfrak d_4$. This problem is equivalent to finding the maximal abelian diagonalizable subgroups of the automorphism group of $\mathfrak d_4$. We prove that there are fourteen by using two different viewpoints. The first approach is computational: we get a full description of the gradings by using a particular implementation of the automorphism group of the Dynkin diagram of $\mathfrak d_4$ and some algebraic groups stuff. The second approach, more qualitative, emphasizes some algebraic aspects, as triality, and it is mostly devoted to gradings involving the outer automorphisms of order three. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0804.1763 | |
| dc.identifier | http://arxiv.org/abs/0804.1763 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158519 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Mathematical Physics | |
| dc.subject | 17B05; 17B70 | |
| dc.title | Fine Gradings on the exceptional Lie algebra $\mathfrak d_4$ | |
| dc.type | text |