Summary of the graded contractions of the Pauli graded \(\text{sl}(2, \mathbb C)\) and \(\text{sl}(3, \mathbb C)\). (English) Zbl 1161.17321

Summary: We consider the Pauli grading of the Lie algebra \(\text{sl}(2, \mathbb C)\) and \(\text{sl}(3, \mathbb C)\). We use a concept of graded contractions to construct non-isomorphic Lie algebras of dimension 3 and 8. We survey methods used to solve the system of contraction equations and to distinguish the results. We show how the symmetry group of the Pauli gradings simplify this task. We present a short overview of the resulting Lie algebras. Complete results will be published elsewhere, see J. Geom. Symmetry Phys. 6, 47–54 (2006; Zbl 1154.17306).


17B70 Graded Lie (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
81R05 Finite-dimensional groups and algebras motivated by physics and their representations


Zbl 1154.17306