Supersolvability of built lattices and Koszulness of generalized Chow rings

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.