Polytopal linear retractions
Authors:
Winfried Bruns and Joseph Gubeladze
Journal:
Trans. Amer. Math. Soc. 354 (2002), 179203
MSC (2000):
Primary 13F20, 14M25; Secondary 52C07
Published electronically:
May 14, 2001
MathSciNet review:
1859031
Fulltext PDF Free Access
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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.uniosnabrueck.de
Joseph Gubeladze
Affiliation:
A. Razmadze Mathematical Institute, Alexidze St. 1, 380093 Tbilisi, Georgia
Email:
gubel@rmi.acnet.ge
DOI:
http://dx.doi.org/10.1090/S0002994701027039
PII:
S 00029947(01)027039
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 MaxPlanckInstitut für Mathematik in Bonn and INTAS, Grant 932618Ext
Article copyright:
© Copyright 2001
American Mathematical Society
