Oleksandra Gasanova

Universität Duisburg-Essen

Chain algebras of finite distributive lattices

Let L be a finite distributive lattice and let t_1,…,t_n denote the elements of its ground set. To each maximal chain C of L one can associate a squarefree monomial m in K[t_1,…,t_n] which equals the product of all t_i belonging to C. We then consider the subalgebra K[m_1,…,m_s], generated by all such monomials, and call it the chain algebra of L. We address some properties of chain algebras in connection to combinatorial properties of the corresponding lattices, and explore the connection of such algebras to Hibi rings. Joint project with Lisa Nicklasson.