Classification of noncommutative monoid structures on normal affine surfaces

2021/06/09 by Boris Bilich, Bilich, Boris · 1 citation
Mathematics · #14M25 (Primary) 14R20 #20F16 (Secondary) #20G15 #20M32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2106.04884

openalex publication_date 2021/06/09 · openalex created_date 2022/08/25 · openalex updated_date 2026/07/28

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.

Cited by

• Root monoids and active algebraic groups

Related

• The structure of normal algebraic monoids
• Algebraic monoid structures on the affine 3-space
• Twisted forms of commutative monoid structures on affine spaces
• Homological Algebra for Commutative Monoids
• Root monoids and active algebraic groups