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The Lefschetz properties / Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe.

By: Harima, Tadahito [author.]Contributor(s): Maeno, Toshiaki [author.] | Morita, Hideaki [author.] | Numata, Yasuhide [author.] | Wachi, Akihito [author.] | Watanabe, Junzo [author.]Material type: Text

TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2080.Description: xix, 250 pages : illustrations ; 24 cmISBN: 9783642382055 (pbk. : alk. paper); 3642382053 (pbk. : alk. paper); 9783642382062 (ebk.)Subject(s): Geometry, Algebraic | Artin ringsDDC classification: 516.35 LOC classification: QA251.3 | .H27 2013QA3 | .L28 no.2080Also issued online.

Contents:

Poset theory -- Basics on the theory of local rings -- Lefschetz properties -- Compete intersections with the SLP -- A generalization of Lefschetz elements -- k-Lefschetz properties -- Cohomology rings -- Invariant theory and Lefschetz property -- The strong Lefschetz property and the SchurWeyl duality.

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.

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Includes bibliographical references (pages 239-246) and index.

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.

Also issued online.

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