The Ring of Regular Functions of an Algebraic Monoid
نویسندگان
چکیده
Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G = GantGaff ∼= (Gant ×Gaff )/Gaff ∩Gant, where Gant is the maximal anti-affine subgroup of G, and Gaff the maximal normal connected affine subgroup of G. In this paper we show that this decomposition extends to a decomposition M = GantMaff ∼= Gant∗Gaff∩GantMaff , whereMaff is the affine submonoidMaff = Gaff . We then use this decomposition to calculateO(M) in terms ofO(Maff) andGaff , Gant ⊂ G. In particular, we determine when M is an anti-affine monoid, that is O(M) = k.
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تاریخ انتشار 2011