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Mathematics - Algebra | The Lefschetz Properties

The Lefschetz Properties

Series: Lecture Notes in Mathematics, Vol. 2080

Harima, T., Maeno, T., Morita, H., Numata, Y., Wachi, A., Watanabe, J.

2013, XIX, 250 p. 20 illus.

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  • This is the first book on the theory of Lefschetz properties
  • This is the first attempt to treat the theory of Lefschetz properties systematically
  • This book shows a wide connection of the Lefschetz properties to other areas of mathematics
  • So, Researchers from various area of mathematics should be interested in this book
  • This book contains many open problems
  • Some new results are contained (Some of them may appear as papers elsewhere. Some of them may not.)
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.

Content Level » Research

Keywords » 13-02, 13A02, 13A50, 06A07, 06A11,14M15,14F99, 14M10, 14L30 - Dilworth number - Schur-Weyl duality - graded Artinian rings - weak and strong Lefschetz propeties

Related subjects » Algebra

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