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Polytopal linear retractions
Author(s):
Winfried
Bruns;
Joseph
Gubeladze
Journal:
Trans. Amer. Math. Soc.
354
(2002),
179-203.
MSC (2000):
Primary 13F20, 14M25;
Secondary 52C07
Posted:
May 14, 2001
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Abstract:
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  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  -theory).
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Additional Information:
Winfried
Bruns
Affiliation:
Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany
Email:
Winfried.Bruns@mathematik.uni-osnabrueck.de
Joseph
Gubeladze
Affiliation:
A. Razmadze Mathematical Institute, Alexidze St. 1, 380093 Tbilisi, Georgia
Email:
gubel@rmi.acnet.ge
DOI:
10.1090/S0002-9947-01-02703-9
PII:
S 0002-9947(01)02703-9
Keywords:
Polytopal algebra,
retracts,
affine semigroup ring,
binomial ideal
Received by editor(s):
January 10, 2000
Received by editor(s) in revised form:
April 10, 2000
Posted:
May 14, 2001
Additional Notes:
The second author was supported by the Max-Planck-Institut für Mathematik in Bonn and INTAS, Grant 93-2618-Ext
Copyright of article:
Copyright
2001,
American Mathematical Society
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