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September 10, 2025

The Lattice property of biclosed sets for infinite root systems

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Authors

JHJeremy Hare-ChangYMYixin MaIDIvan Dimitrov

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Overview

This work explores biclosed sets generalizing inversion sets in Kac–Moody root systems, revealing structural limitations.

Key Points

  • Biclosed sets exhibit unique lattice properties distinct from finite root systems.
  • Investigation reveals that the '2-out-of-3 rule' fails for sets with imaginary roots.
  • Two notions of closure provide a framework to understand the structure of biclosed sets.
  • Biclosed sets extend geometric insights from inversion sets to the realm of infinite root systems.

Cite This Study

Hare-Chang et al. (2025) studied this question.

synapsesocial.com/papers/68c1d98f54b1d3bfb60fb759https://doi.org/10.24908/iqurcp19826
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