DECOMPOSITION THEOREMS FOR A GENERALIZATION OF THE HOLONOMY LIE ALGEBRA OF AN ARRANGEMENT

摘要

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.