Gradings on the Albert Algebra and on $f_4$

By C. Draper, C'andido Mart'in. 2007

61 citations recorded by the source corpus.

We study group gradings on the Albert algebra and on the simple exceptional Lie algebra $\frak{f}_4$ over algebraically closed fields of characteristic zero. There are eight nontoral nonequivalent gradings on the Albert algebra (three of them being fine) and nine on $\frak{f}_4$ (also three of them fine).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4ef48e9198f3e3966de1765530c2b941558df606

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. A. Pianzola
2. S. Berman
3. J. Faulkner
4. B. Allison
5. Mikhail Kochetov
6. Yōji Yoshii
7. Michael Lau
8. Yung Gao

In Geometry and Topology

1. A. Pianzola
2. S. Berman
3. J. Faulkner
4. B. Allison
5. Mikhail Kochetov
6. Yōji Yoshii
7. Michael Lau
8. Yung Gao

In Mathematical Physics

1. B. Allison
2. Mikhail Kochetov
3. S. Berman
4. A. Pianzola
5. J. Faulkner

Citations in the corpus

• Gradings on Finite-Dimensional Simple Lie Algebras (2009, methodology): “It turns out that in some cases non-toral fine gradings can be explicitly constructed as refinements of toral gradings [19, 20 ].”
• Multiloop realization of extended affine Lie algebras and Lie tori (2007, methodology): “Acknowledgement: The authors thank Christina Draper for a very helpful conversation related to her work with Candido Martin in [ DM ] on gradings of F4.”