Decomposition theorems for a generalization of the holonomy Lie algebra of an arrangement
| Autor: | Löfwall, Clas |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Communications in Algebra 44(11) 2014 |
| Druh dokumentu: | Working Paper |
| Popis: | In [7, Papadima and Suciu, When does the associated graded Lie algebra of an arrangement group decompose? Comment. Math. Helv. {\bf 81:4} (2006), 859--875] it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through origo 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 [7]. Comment: substantial changes are made. The connection with matroids is included in the beginning. The definition of "replacement" has changed to cover cases with local Lie algebras on two generators that are not abelian. Thus the example in the beginning has been moved and it is now a consequence of the theory |
| Databáze: | arXiv |
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