Abstract:
The resonance varieties, the holonomy Lie algebra, and the holonomy
Chen Lie algebra associated with the Orlik-Solomon algebra of a
matroid provide an algebraic lens through which to examine the rich
combinatorial structure of matroids and their geometric realizations
as complex hyperplane arrangements. In this survey paper, we
emphasize the commonalities between these objects but also the
possible ways in which realizable and non-realizable matroids
differ, leading to some open questions.
Key Words: Matroid, hyperplane arrangement,
Orlik-Solomon algebra, resonance variety, decomposable matroid,
holonomy Lie algebra, Chen ranks, Koszul module.
2020 Mathematics Subject Classification: Primary
52C35; Secondary 14N20, 16W70, 17B70, 20F14, 20F40, 52B40, 57M07.
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