The Lefschetz Properties

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...

Full description

Bibliographic Details
Main Authors: Harima, Tadahito, Maeno, Toshiaki (Author), Morita, Hideaki (Author), Numata, Yasuhide (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2013, 2013
Edition:1st ed. 2013
Series:Lecture Notes in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Description
Summary: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 last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically
Physical Description:XIX, 250 p. 20 illus online resource
ISBN:9783642382062