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Decomposition Theorems for a Generalization of the Holonomy Lie Algebra of an Arrangement

In the article “When does the Associated graded Lie algebra of an Arrangement Group Decompose?” by Stefan Papadima and Alexander Suciu [7], it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through origin decomposes as a direct product of Lie algebras in degree at least two if and only if a certain (computable) condition is fulfilled. We prove similar results for a class of Lie algebras which is a generalization of the holonomy Lie algebras. The proof methods are the same as in the article cited above.