Polytopal linear retractions

Authors:
Winfried Bruns and Joseph Gubeladze

Journal:
Trans. Amer. Math. Soc. **354** (2002), 179-203

MSC (2000):
Primary 13F20, 14M25; Secondary 52C07

DOI:
https://doi.org/10.1090/S0002-9947-01-02703-9

Published electronically:
May 14, 2001

MathSciNet review:
1859031

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-01-02703-9

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

Published electronically:
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

Article copyright:
© Copyright 2001
American Mathematical Society