Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

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.

💡 Research Summary

The paper introduces a new family of non‑associative algebras, called Integro‑Derivation Dzhumadildaev (IDD) algebras, obtained by applying differential and integral operators to the classical polynomial algebra K