The Lefschetz Properties

  • Tadahito Harima
  • Toshiaki Maeno
  • Hideaki Morita
  • Yasuhide Numata
  • Akihito Wachi
  • Junzo Watanabe

Part of the Lecture Notes in Mathematics book series (LNM, volume 2080)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 1-38
  3. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 39-95
  4. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 97-140
  5. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 141-156
  6. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 157-170
  7. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 171-188
  8. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 189-199
  9. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 201-209
  10. Tadahito Harima, Toshiaki Maeno, Hideaki Morita, Yasuhide Numata, Akihito Wachi, Junzo Watanabe
    Pages 211-234
  11. Back Matter
    Pages 235-252

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Tadahito Harima
    • 1
  • Toshiaki Maeno
    • 2
  • Hideaki Morita
    • 3
  • Yasuhide Numata
    • 4
  • Akihito Wachi
    • 5
  • Junzo Watanabe
    • 6
  1. 1.Department of Mathematical EducationNiigata UniversityNishi-KuJapan
  2. 2.Meijo University Department of MathematicsNagoyaJapan
  3. 3.Muroran Institute of TechnologyMuroranJapan
  4. 4.Department of Mathematical SciencesShinshu UniversityMatsumotoJapan
  5. 5.Hokkaido University of Education Department of MathematicsKushiroJapan
  6. 6.Tokai University Department of MathematicsHiratsukaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-38206-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-38205-5
  • Online ISBN 978-3-642-38206-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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