The Lefschetz Properties

• Main Authors: Harima, Tadahito. (Author), Maeno, Toshiaki. (Author), Morita, Hideaki. (Author), Numata, Yasuhide. (Author), Wachi, Akihito. (Author), Watanabe, Junzo. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2080
• Subjects: Mathematics.; Algebra.; Geometry, algebraic.; Combinatorics.; Algebraic Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-38206-2

This is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the las...

Table of Contents:

• Introduction and Historical Note
• 1. Poset Theory
• 2. Basics on the Theory of Local Rings
• 3. Lefschetz Properties
• 4. Compete Intersections with the SLP
• 5.�A Generalization of Lefschetz Elements
• 6.�k-Lefschetz Properties
• 7.�Cohomology Rings
• 8.� Invariant Theory and Lefschetz Property
• 9.�The Strong Lefschetz Property and the SchurWeyl Duality.��.