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- W2413609758 abstract "The first main objective of work was to create a combinatorial answer to an essential question; How Terao generalization of class of supersolvable arrangements preserved tensor factorization of O-S algebra?, by finding a relation among several bases of O-S algebra. This was achieved in two parts. First, class of factored arrangements was classified in two subclasses, subclass of completely factored arrangements and subclass of factored arrangement that not completely factored. Our classification criteria was, the existence of an ordering on hyperplanes of a factored arrangement such that set of all monomials that related to sections of a factorization on forms an NBC basis of O-S algebra as a free The second part was, a comparison among structures of O-S complex, NBC complex and partition complex. In spite of, our classification criteria was failed of second subclass of factored arrangement that not completely factored, existence of a one to one correspondence between set of all NBC bases of and set of all sections of a factorization on , provides a tensor factorization fashion to O-S algebra. The second main aim of work was to prove that our classification is compatible with product construction for arrangements, by constructing O-S complex, NBC complex and partition complex of reducible factored arrangements. Finally, several illustrations and applications were indicated. Keywords: Hyperplane arrangement, Supersolvable arrangement, factored (Nice) arrangement, Orlik-Solomon algebra, NBC module and Partition tensor module." @default.
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- W2413609758 date "2016-01-01" @default.
- W2413609758 modified "2023-09-26" @default.
- W2413609758 title "On The Class Of Factored Arrangements" @default.
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