Open Access
Polytopal Linear Algebra
Winfried Bruns,Joseph Gubeladze +1 more
- 01 Jan 2002
- Vol. 43, Iss: 2, pp 479-500
TL;DR: In this paper, the authors investigated similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory and showed that it is trivial for fields.
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Abstract: 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 (3, 4, 5) The higher K-theoretic aspects of polytopal linear objects will be treated in (6, 7)
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Citations
Higher polyhedral K-groups
Winfried Bruns,Joseph Gubeladze +1 more
TL;DR: In this article, higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras, are developed.
10
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Polytopes and k-theory
Winfried Bruns,Joseph Gubeladze +1 more
TL;DR: In this paper, a conjecture is proposed on the structure of higher polyhedral K-groups for certain classes of polytopes for which the coincidence of Quillen's and Volodin's theories is known.
3
Polytopal Linear Groups and Balanced 3-Polytopes
TL;DR: In this article, a list of all possibly occurring E-equivalence classes of three-dimensional balanced polytopes of dimension 3 has been given, provided P is a Col-divisible balanced polytope of dimension three.
1
Tame homomorphisms of polytopal rings
Viveka Erlandsson
- 01 Jan 2008
TL;DR: The tameness conjecture as mentioned in this paper describes an arbitrary graded k-algebra homomorphism of polytopal rings, which can be seen as a generalization of the notion of product polytopes.
Update on toric geometry
David A. Cox
- 01 Jan 2002
TL;DR: This paper will survey some recent work on toric varieties to help the reader understand how the papers in this volume relate to current trends in toric geometry.
References
•Book
Categories for the Working Mathematician
Saunders Mac Lane
- 01 Jan 1971
TL;DR: In this article, the authors present a table of abstractions for categories, including Axioms for Categories, Functors, Natural Transformations, and Adjoints for Preorders.
10.5K
•Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
- 01 Jan 1993
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.
3.3K
Sous-groupes algébriques de rang maximum du groupe de Cremona
TL;DR: In this article, Gauthier-Villars implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Polytopal linear retractions
Winfried Bruns,Joseph Gubeladze +1 more
TL;DR: In this paper, the authors investigated graded retracts of polytopal algebras (essentially the homogeneous rings of affine cones over projective toric varieties).
Higher polyhedral K-groups
Winfried Bruns,Joseph Gubeladze +1 more
TL;DR: In this article, higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras, are developed.
10