Classification of noncommutative monoid structures on normal affine surfaces
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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.References
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Additional Information
- Boris Bilich
- Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3–5, 37073 Göttingen, Germany; and Laboratory on Algebraic Transformation Groups, HSE University, 11 Pokrovsky Bulvar, 109028 Moscow, Russia
- ORCID: 0000-0002-5353-428X
- Email: bilichboris1999@gmail.com
- Received by editor(s): July 15, 2021
- Received by editor(s) in revised form: October 11, 2021
- Published electronically: July 15, 2022
- Communicated by: Jerzy Weyman
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4129-4144
- MSC (2020): Primary 20M32, 14M25; Secondary 14R20, 20G15, 20F16
- DOI: https://doi.org/10.1090/proc/16083
- MathSciNet review: 4470163