Polytopal linear algebra
| dc.creator | Bruns, Winfried | |
| dc.creator | Gubeladze, Joseph | |
| dc.date | 2000-02-03 | |
| dc.date | 2001-07-30 | |
| dc.date.accessioned | 2026-07-07T04:33:34Z | |
| dc.date.available | 2026-07-07T04:33:34Z | |
| dc.description | We investigate similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory. In Section 2 we introduce the notion of a polytopal Picard group and show that it is trivial for fields. The coincidence of this group with the ordinary Picard group for general rings remains an open question. In Section 3 we survey some of the previous results on the automorphism groups and retractions. These results support a general conjecture proposed in Section 4 about the nature of arbitrary homomorphisms of polytopal algebras. Thereafter a further confirmation of this conjecture is presented by homomorphisms defined on Veronese singularities. This is a continuation of the project started in our papers "Polytopal linear groups" (J. Algebra 218 (1999), 715--737), "Polytopal linear retractions" preprint, math.AG/0001049) and "Polyhedral algebras, arrangements of toric varieties, and their groups" (preprint, http://www.mathematik.uni-osnabrueck.de/K-theory/0232/index.html). The higher $K$-theoretic aspects of polytopal linear objects will be treated in "Polyhedral $K$-theory" (in preparation). | |
| dc.description | 21 pages, uses pstricks and P. Taylor's CD package. Beitr. Algebra Geom., to appear | |
| dc.identifier | https://arxiv.org/abs/math/0002024 | |
| dc.identifier | http://arxiv.org/abs/math/0002024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58622 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F99, 14M25 | |
| dc.title | Polytopal linear algebra | |
| dc.type | text |