Linear flags and Koszul filtrations

Abstract

We show that the graded maximal ideal of a graded $K$-algebra $R$ has linear quotients for a suitable choice and order of its generators if the defining ideal of $R$ has a quadratic Gröbner basis with respect to the reverse lexicographic order, and show that this linear quotient property for algebras defined by binomial edge ideals characterizes closed graphs. Furthermore, for algebras defined by binomial edge ideals attached to a closed graph and for join-meet rings attached to a finite distributive lattice we present explicit Koszul filtrations.

References in corpus (1)

• On closed graphs II

Cited by in corpus (6)

• On closed graphs II
• Enhanced Koszul properties in Galois cohomology
• Right-angled Artin groups and enhanced Koszul properties
• Reverse lexicographic Gröbner bases and strongly Koszul toric rings
• Some Computations for Binomial Edge Ideals and Koszul Duality
• A Koszul filtration for the second squarefree Veronese subring