The center of thin Gaussian groups
A `thin Gaussian monoid' is a cancellative monoid \(M\) in which \(1\) is the only invertible element, in which least common multiples exist, and which admits a finite generating set which is closed under the operation \(\setminus\), where for any \(a,b\in M\), \(a(a\setminus b)\) is the right lcm of \(a\) and \(b\). A `thin Gaussian group' is the group of fractions of a thin Gaussian monoid. Thin Gaussian groups are a generalization of Artin groups of finite type (e.g., the braid groups).NEWLINENEWLINENEWLINEThe author analyzes the centers of thin Gaussian groups. He identifies a certain subclass (the `\(\Delta\)-pure' thin Gaussian groups) whose centers are infinite cyclic, generated by a power of an element \(\Delta\) which is analagous to the fundamental element of a finite-type Artin group. He then shows that every thin Gaussian group is a certain kind of product of \(\Delta\)-pure thin Gaussian groups.
scientific article; zbMATH DE number 1721739
scientific article