Graded contractions of the Gell-Mann graded sl(3,C)

Abstract

The Gell-Mann grading, one of the four gradings of sl(3,C) that cannot be further refined, is considered as the initial grading for the graded contraction procedure. Using the symmetries of the Gell-Mann grading, the system of contraction equations is reduced and solved. Each non-trivial solution of this system determines a Lie algebra which is not isomorphic to the original algebra sl(3,C). The resulting 53 contracted algebras are divided into two classes - the first is represented by the algebras which are also continuous Inonu-Wigner contractions, the second is formed by the discrete graded contractions.

21 pages

References in corpus (6)

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Cited by in corpus (3)

• Generic graded contractions of Lie algebras
• Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8
• Linear models of the exceptional Lie algebra ${\mathfrak{e}}_8$