Classification of noncommutative monoid structures on normal affine surfaces

Bilich, Boris

doi:10.1090/proc/16083

Classification of noncommutative monoid structures on normal affine surfaces
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Proc. Amer. Math. Soc. 150 (2022), 4129-4144 Request permission

Abstract:

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by a comultiplication formula involving Demazure roots. We also give descriptions of opposite monoids, quotient monoids, and boundary divisors.

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