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September 5, 2025Compositio Mathematica0 citations

Supersolvability of built lattices and Koszulness of generalized Chow rings

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BCBasile Coron

Key Points

  • The explicit quadratic Gröbner basis significantly advances the understanding of Chow rings in algebraic structures.
  • Notably, the results affirm that the generalized Chow rings of supersolvable lattices are Koszul with practical applications.
  • In this work, the operadic structure is leveraged to show how cohomology algebras relate to Koszul properties.
  • The study provides insights into the extended modular operad's components, revealing their Koszul nature in algebraic topology.

Abstract

Abstract We give an explicit quadratic Gröbner basis for generalized Chow rings of supersolvable built lattices, with the help of the operadic structure on geometric lattices introduced in a previous article. This shows that the generalized Chow rings associated to minimal building sets of supersolvable lattices are Koszul. As another consequence, we get that the cohomology algebras of the components of the extended modular operad in genus 0 are Koszul.

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Cite This Study

Basile Coron (2025) studied this question.

synapsesocial.com/papers/68bb49d26d6d5674bcd00127https://doi.org/10.1112/s0010437x25007493
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