Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

TL;DR

This paper explores new classes of infinite-dimensional simple conservative algebras derived from polynomial algebras using derivation and integration, expanding understanding of their structure and derivations.

Contribution

It introduces novel classes of algebras constructed from polynomials and characterizes their derivations, advancing algebraic theory.

Findings

Discovered new infinite-dimensional simple conservative algebras.

Described derivations of these algebras of ranks 1 and 2.

Extended the algebraic framework from polynomial algebras.

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.