Gradings on the exceptional Lie algebras \(F_4\) and \(G_2\) revisited

DOI10.4171/RMI/691zbMath1303.17019arXiv1009.1218MaRDI QIDQ446411

Mikhail Kochetov, Alberto Elduque

Publication date: 6 September 2012

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1218

zbMATH Keywords

Weyl groupoctonionsAlbert algebragraded algebrafine gradingF4G2

Mathematics Subject Classification ID

Exceptional (super)algebras (17B25) Graded Lie (super)algebras (17B70)

Related Items (16)

Gradings on Lie triple systems related to exceptional Lie algebras ⋮ Gradings on the simple real Lie algebras of types \(G_2\) and \(D_4\) ⋮ Fine gradings on simple exceptional Jordan pairs and triple systems ⋮ Some special features of Cayley algebras, and \(G_2\), in low characteristics ⋮ On arbitrarily graded rings ⋮ Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra. ⋮ Gradings on the Lie algebra \(D_4\) revisited ⋮ Fine gradings and their Weyl groups for twisted Heisenberg Lie superalgebras ⋮ Abelian groups gradings on null-filiform and one-parametric filiform Leibniz algebras ⋮ Gradings and symmetries on Heisenberg type algebras ⋮ COUNTING FINE GRADINGS ON MATRIX ALGEBRAS AND ON CLASSICAL SIMPLE LIE ALGEBRAS ⋮ An overview of ne gradings on simple Lie algebras ⋮ On nonassociative graded-simple algebras over the field of real numbers ⋮ Fine gradings and gradings by root systems on simple Lie algebras ⋮ Gradings on Composition Superalgebras ⋮ Augmented \(n\)-ary maps and their applications to graded \(n\)-ary algebraic structures

Cites Work

• Classification of group gradings on simple Lie algebras of types \(\mathcal A\), \(\mathcal B\), \(\mathcal C\) and \(\mathcal D\)
• Group gradings on simple Lie algebras in positive characteristic
• Group gradings on associative algebras

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