Polytopal linear retractions

Autor(en): Bruns, W 
Gubeladze, J
Stichwörter: affine semigroup ring; binomial ideal; Mathematics; polytopal algebra; retracts
Erscheinungsdatum: 2002
Herausgeber: AMER MATHEMATICAL SOC
Journal: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 354
Ausgabe: 1
Startseite: 179
Seitenende: 203
Zusammenfassung: 
We investigate graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties) as polytopal analogues of vector spaces. In many cases we show that these retracts are again polytopal algebras and that codimension 1 retractions factor through retractions preserving the semigroup structure. We expect that these results hold in general. This paper is a part of the project started by the authors in 1999, where we investigate the graded automorphism groups of polytopal algebras. Part of the motivation comes from the observation that there is a reasonable `polytopal' generalization of linear algebra (and, subsequently, that of algebraic K-theory).
ISSN: 00029947
DOI: 10.1090/S0002-9947-01-02703-9

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