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A Survey on Koszul Algebras and Koszul Duality

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Leavitt Path Algebras and Classical K-Theory

Part of the book series: Indian Statistical Institute Series ((INSIS))

Abstract

In this survey article, we discuss the theory of Koszul algebras and Koszul duality. Koszul property plays an important role in various topics such as commutative and noncommutative algebra, geometry, topology, Lie algebras, representation theory, combinatorics and semigroup rings. Most of the results in this survey article are already known or are easy corollaries of known results. We collect these results and we discuss some proofs. Several survey articles, notably [22, 13,14,15, 31], and a book on quadratic algebras [36] contain valuable material to the theory of Koszul algebras or Koszul duality. Keeping these survey articles in mind, the focus has been to collect new results on Koszulness of diagonal subalgebras, its interaction with Pólya frequency sequence, and monomial projective curves.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Hyderabad, Sangareddy, Kandi, 502285, India

    Neeraj Kumar

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  1. Neeraj Kumar
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Correspondence to Neeraj Kumar .

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Editors and Affiliations

  1. Department of Mathematics, Cochin University of Science and Technology, Cochin, Kerala, India

    A. A. Ambily

  2. Centre for Research in Mathematics, Western Sydney University, Sydney, NSW, Australia

    Roozbeh Hazrat

  3. Statistics and Mathematics Unit, Indian Statistical Institute, Bengaluru, Karnataka, India

    B. Sury

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Kumar, N. (2020). A Survey on Koszul Algebras and Koszul Duality. In: Ambily, A., Hazrat, R., Sury, B. (eds) Leavitt Path Algebras and Classical K-Theory. Indian Statistical Institute Series. Springer, Singapore. https://doi.org/10.1007/978-981-15-1611-5_7

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