Applications of Groebner bases techniques

09/02/2018, 00:00 in MAP/0G/018

Iyudu, Natalja (University of Edinburgh)


Abstract:

We describe various applications of the noncommutative Groebner bases techniques for  calculation of growth and Hilbert series of quadratic algebras, appearing as operator algebras or otherwise in many applications such as physics, integrable systems, etc. Examples include Sklyanin algebras, potential algebras (or vacualgebras), homology of moduli spaces of pointed curves given by Keel relations, etc. On the basis of calculation of Hilbert series various homological properties such as Koszulity and Calabi-Yau can be established. Moreover, if time permits, we touch upon connections of word combinatorics and Groebner basis techniques, as well as operadic  generalisations of Groebner bases.