Growth of associated monomial algebras and Manturov groups

It is well-known that an associative algebra shares the same growth and Gelfand-Kirillov dimension (GK-dimension) as its associated monomial algebra with respect to a degree-lexicographic order. In this talk, we discuss the relationship between the GK-dimension of an associative algebra and that of its associated monomial algebra with respect to a monomial order. As an application, we study the growth of Manturov groups, which were introduced by V. Manturov in 2015.