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.
Authors and Affiliations
Department of Mathematical Education, Niigata University, Nishi-Ku, Japan
Tadahito Harima
Meijo University Department of Mathematics, Nagoya, Japan
Toshiaki Maeno
Muroran Institute of Technology, Muroran, Japan
Hideaki Morita
Department of Mathematical Sciences, Shinshu University, Matsumoto, Japan
Yasuhide Numata
Hokkaido University of Education Department of Mathematics, Kushiro, Japan
Akihito Wachi
Tokai University Department of Mathematics, Hiratsuka, Japan
