Associated Lie algebras and graded contractions of the Pauli graded \({\mathfrak {sl}}(3,\mathbb C)\). (English) Zbl 1154.17306

The authors determine the graded contractions of the eight-dimensional Lie algebra \(A_2=\mathfrak{sl}(3,\mathbb C)\) for its \(\mathbb Z_3\times \mathbb Z_3\)-Pauli)-grading using – in addition to the usual tools – some special cases of generalized derivations, introduced by Leger and Luks, to decide which of their resulting Lie algebras are equivalent.


17B70 Graded Lie (super)algebras
17B05 Structure theory for Lie algebras and superalgebras