FROM BRACES TO PRE-LIE RINGS

Aner Shalev; Agata Smoktunowicz

doi:10.1090/proc/16693

FROM BRACES TO PRE-LIE RINGS

Aner Shalev, Agata Smoktunowicz

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

Let A be a brace of cardinality pⁿ where p > n + 1 is prime and let ann(p²) be the set of elements of additive order at most p² in this brace. We construct a pre-Lie ring related to the brace A/ann(p²). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p²) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.

Original language	English
Pages (from-to)	1545-1559
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	152
Issue number	4
DOIs	https://doi.org/10.1090/proc/16693
State	Published - 1 Apr 2024

Bibliographical note

Publisher Copyright:
© 2024 American Mathematical Society.

Access to Document

10.1090/proc/16693

Cite this

@article{e9aaa022ab41483a858b8282a39a760e,

title = "FROM BRACES TO PRE-LIE RINGS",

abstract = "Let A be a brace of cardinality pn where p > n + 1 is prime and let ann(p2) be the set of elements of additive order at most p2 in this brace. We construct a pre-Lie ring related to the brace A/ann(p2). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p2) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.",

author = "Aner Shalev and Agata Smoktunowicz",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society.",

year = "2024",

month = apr,

day = "1",

doi = "10.1090/proc/16693",

language = "אנגלית",

volume = "152",

pages = "1545--1559",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - FROM BRACES TO PRE-LIE RINGS

AU - Shalev, Aner

AU - Smoktunowicz, Agata

PY - 2024/4/1

Y1 - 2024/4/1

N2 - Let A be a brace of cardinality pn where p > n + 1 is prime and let ann(p2) be the set of elements of additive order at most p2 in this brace. We construct a pre-Lie ring related to the brace A/ann(p2). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p2) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.

AB - Let A be a brace of cardinality pn where p > n + 1 is prime and let ann(p2) be the set of elements of additive order at most p2 in this brace. We construct a pre-Lie ring related to the brace A/ann(p2). In the case of strongly nilpotent braces of nilpotency index k < p the brace A/ann(p2) can be recovered by applying the construction of the group of flows to the resulting pre-Lie ring. We do not know whether or not our construction is related to the group of flows when applied to braces which are not right nilpotent.

UR - http://www.scopus.com/inward/record.url?scp=85186670256&partnerID=8YFLogxK

U2 - 10.1090/proc/16693

DO - 10.1090/proc/16693

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85186670256

SN - 0002-9939

VL - 152

SP - 1545

EP - 1559

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

FROM BRACES TO PRE-LIE RINGS

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this