3:45PM: Isotonian AlgebrasMina BigdeliTo a pair P and Q of finite posets we attach the toric ring K[P, Q] whose generators are in bijection to the isotone maps from P to Q. This class of algebras, called isotonian, are natural generalizations of the socalled Hibi rings. In this talk we introduce isotonian algebras and then state their Krull dimension. We discuss particular classes of posets P and Q for which the toric ring K[P, Q] is normal, and the classes that the defining ideal of their isotonian algebras admits a quadratic Gröbner basis. This talk is based on a joint work with J. Herzog, T. Hibi, A. Qureshi and A. Shikama.
