Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8

Abstract

Graded contractions of certain non-toral ${\mathbb{Z}}_2^3$-gradings on the simple Lie algebras $\mathfrak{so}(7,\mathbb{C})$ and $\f{so}(8,\mathbb C)$ are classified up to two notions of equivalence. In particular, there arise two large families of Lie algebras (the majority of which are solvable) of dimensions 21 and 28. This is achieved as a significant generalization of the classification of related graded contractions on ${\mathfrak{g}}_2$, the derivation algebra of the octonion algebra. Many of the results can be further extended to any \emph{good} ${\mathbb{Z}}_2^3$-grading on an arbitrary Lie algebra.

21 pages

References in corpus (2)

• Graded contractions of the Pauli graded sl(3,C)
• Generic graded contractions of Lie algebras

Cited by in corpus (1)

• Generic graded contractions of Lie algebras