| dc.creator | Cordovil, Raúl | |
| dc.creator | Forge, David | |
| dc.date | 2005-08-01 | |
| dc.date.accessioned | 2019-05-03T12:36:44Z | |
| dc.date.available | 2019-05-03T12:36:44Z | |
| dc.identifier | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1539 | |
| dc.identifier.uri | http://revistaschilenas.uchile.cl/handle/2250/84270 | |
| dc.description | The Orlik-Solomon algebra of a matroid M is the quotient of the exterior algebra on the points by the ideal 𝔍(M) generated by the boundaries of the circuits of the matroid. There is an isomorphism between the Orlik-Solomon algebra of a complex matroid and the cohomology of the complement of a complex arrangement of hyperplanes. In this article a generalization of the Orlik-Solomon algebras, called χ-algebras, are considered. These new algebras include, apart from the Orlik-Solomon algebras, the Orlik-Solomon-Terao algebra of a set of vectors and the Cordovil algebra of an oriented matroid. To encode an important property of the “no broken circuit bases” of the Orlik-Solomon-Terao algebras, Andr´as Szenes has introduced a particular type of bases, the so called “diagonal bases”. This notion extends naturally to the χ-algebras. We give a survey of the results obtained by the authors concerning the construction of Gr¨obner bases of 𝔍χ(M) and diagonal bases of Orlik-Solomon type algebras and we present the combinatorial analogue of an “iterative residue formula” introduced by Szenes. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1539/1393 | |
| dc.source | CUBO, A Mathematical Journal; Vol. 7 Núm. 2 (2005): CUBO, A Mathematical Journal; 1-20 | es-ES |
| dc.source | CUBO, A Mathematical Journal; Vol 7 No 2 (2005): CUBO, A Mathematical Journal; 1-20 | en-US |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.title | Gr¨obner and diagonal bases in Orlik-Solomon type algebras | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
