CLASSIFICATION OF NONCOMMUTATIVE MONOID STRUCTURES ON NORMAL AFFINE SURFACES

Boris Bilich

doi:10.1090/proc/16083

CLASSIFICATION OF NONCOMMUTATIVE MONOID STRUCTURES ON NORMAL AFFINE SURFACES

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	4129-4144
Number of pages	16
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	10
DOIs	https://doi.org/10.1090/proc/16083
State	Published - 1 Oct 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 American Mathematical Society.

Keywords

Algebraic monoid
Demazure root
grading
locally nilpotent derivation
solvable algebraic group
toric variety

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc/16083

Cite this

@article{34f218f160324c198531d34ed71880c6,

title = "CLASSIFICATION OF NONCOMMUTATIVE MONOID STRUCTURES ON NORMAL AFFINE SURFACES",

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.",

keywords = "Algebraic monoid, Demazure root, grading, locally nilpotent derivation, solvable algebraic group, toric variety",

author = "Boris Bilich",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society.",

year = "2022",

month = oct,

day = "1",

doi = "10.1090/proc/16083",

language = "English",

volume = "150",

pages = "4129--4144",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "10",

}

TY - JOUR

T1 - CLASSIFICATION OF NONCOMMUTATIVE MONOID STRUCTURES ON NORMAL AFFINE SURFACES

AU - Bilich, Boris

PY - 2022/10/1

Y1 - 2022/10/1

N2 - 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.

AB - 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.

KW - Algebraic monoid

KW - Demazure root

KW - grading

KW - locally nilpotent derivation

KW - solvable algebraic group

KW - toric variety

UR - http://www.scopus.com/inward/record.url?scp=85137628335&partnerID=8YFLogxK

U2 - 10.1090/proc/16083

DO - 10.1090/proc/16083

M3 - Article

AN - SCOPUS:85137628335

SN - 0002-9939

VL - 150

SP - 4129

EP - 4144

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

CLASSIFICATION OF NONCOMMUTATIVE MONOID STRUCTURES ON NORMAL AFFINE SURFACES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this