Classification of noncommutative monoid structures on normal affine surfaces. (English) Zbl 1512.20217
Summary: In 2021, S. Dzhunusov and Y. Zaitseva [Forum Math. 33, No. 1, 177–191 (2021; Zbl 1464.14066)] 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.
MSC:
| 20M32 | Algebraic monoids |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 20G15 | Linear algebraic groups over arbitrary fields |
Keywords:
algebraic monoid; toric variety; solvable algebraic group; Demazure root; grading; locally nilpotent derivationCitations:
Zbl 1464.14066References:
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