A braid-like presentation of the integral Steinberg group of type C_2

Christian Kassel (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We show that the Steinberg group $\text{St}(C_2,{\mathbb Z})$ associated with the Lie type $C_2$ and with integer coefficients can be realized as a quotient of the braid group $B_6$ by one relation. As an application we give a new braid-like presentation of the symplectic modular group $\text{Sp}_4({\mathbb Z})$.

Domaines: Théorie des groupes [math.GR]

Christian Kassel. A braid-like presentation of the integral Steinberg group of type C_2. Journal of Algebra, 2020, ⟨10.1016/j.jalgebra.2020.09.015⟩. ⟨hal-02880734v2⟩