2025/01/23 by Musson, Ian M.
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2501.13510
For certain actions of the Weyl groupoid \mathfrakW from [Sergeev and Veselov, Grothendieck rings of basic classical Lie superalgebras, Ann Math, 2011] on an affine variety X, geometric properties of the map π: X \longrightarrow Y= Spec O(X)^\mathfrakW were studied in [Musson, On the geometry of some algebras related to the Weyl groupoid, Contemp. Math. 2024], In this paper we show that if the base field \mathtt k is uncountable, the map π is a geometric quotient which is universal in the category of \mathtt k-schemes. To do this we adapt a result from [Mumford, Fogarty, Kirwan, 1994], showing that a geometric quotient is universal in the category of \mathtt k-schemes, to quotients by groupoids and more generally by equivalence relations. In our approach a key role is played by the closed points and Jacobson schemes.