Polytopes, Rings, and K-Theory

• Main Authors: Gubeladze, Joseph (Author), Bruns, Winfried (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Edition: 1.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Commutative algebra.; Commutative rings.; K-theory.; Convex geometry.; Discrete geometry.; Commutative Rings and Algebras.; K-Theory.; Convex and Discrete Geometry.

This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses severa...

Table of Contents:

• I Cones, monoids, and triangulations
• Polytopes, cones, and complexes
• Affine monoids and their Hilbert bases
• Multiples of lattice polytopes
• II Affine monoid algebras
• Monoid algebras
• Isomorphisms and automorphisms
• Homological properties and Hilbert functions
• Gr#x00F6;bner bases, triangulations, and Koszul algebras
• III K-theory
• Projective modules over monoid rings
• Bass#x2013;Whitehead groups of monoid rings
• Varieties.