Join-meet binomial algebras of distributive lattices
Barbara Betti, Takayuki Hibi
TL;DR
This paper studies the algebraic structure of join-meet binomial algebras derived from finite distributive lattices, focusing on when their defining ideals are generated by quadratic binomials within the framework of algebras with straightening laws.
Contribution
It characterizes conditions under which the defining ideal of these algebras is generated by quadrics, advancing understanding of their algebraic properties.
Findings
Identifies criteria for quadratic generation of the defining ideal.
Connects the structure of distributive lattices with algebraic properties.
Provides insights into algebras with straightening laws for these lattices.
Abstract
We investigate the defining ideal of the algebra over a field generated by the join-meet binomials coming from a finite distributive lattice. In the frame of algebras with straightening laws, the problem when the defining ideal is generated by quadrics is studied.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Coding theory and cryptography