Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 14 Mar 2026Embargo end date: 01 Jan 2026 English Publisher:Centre pour la Communication Scientifique Directe (CCSD)Journal:Communications in Mathematics, volume Volume 34 (2026), Issue 1 (eissn: 2336-1298,

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Authors: Kaygorodov, Ivan; Uzakbaev, Naurizbay;

doi: 10.46298/cm.17612 , 10.48550/arxiv.2603.20302 , 10.5281/zenodo.18834377 , 10.5281/zenodo.18834376

Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

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Abstract

This paper introduces and investigates some properties of algebras constructed from the algebra of polynomials via derivation and integration operators using a process presented by Dzhumadildaev in a previous work. In particular, we discover new classes of infinite-dimensional simple conservative algebras and describe derivations of these algebras of ranks $1$ and $2$.

Keywords

Rings and Algebras (math.RA), 17A30, FOS: Mathematics, derivation, Rota-Baxter operator, algebra of polynomials, conservative algebra

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