On the Global Dimension of Incidence Algebras of Finite Lattices

Key Points

• This work aims to determine the relationship between the order dimension of finite lattices and the global dimension of their incidence algebras.
• Analysis of finite lattices of order dimension d.
• Demonstration with a specific family of finite posets.
• The global dimension of the incidence algebra is shown to be at most d.
• An explicit family of finite posets illustrates that the inequality does not generally hold when not constrained to lattices.