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Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

Ivan Kaygorodov, Naurizbay Uzakbaev

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.

Integro-derivation Dzhumadildaev algebras: from the algebra of polynomials

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.
Paper Structure (14 sections, 1 equation)

This paper contains 14 sections, 1 equation.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The multiplication table of IDD algebras from polynomials
  4. Simple, perfect and nilpotent IDD algebras
  5. Conservative IDD algebras
  6. Derivation of IDD algebras of rank 1
  7. Derivations of IDD(Kx_n,1,0)
  8. Derivations of IDD(Kx̂_n,0,-1)
  9. Derivation of IDD algebras of rank 2
  10. Derivations of IDD(Kx̂_n,2,0)
  11. Derivations of IDD(Kx̂_n,1,1)
  12. Derivations of IDD(Kx̂_n,1,-1)
  13. Derivations of IDD(Kx̂_n,-1,-1)
  14. Derivations of IDD(Kx̂_n,0,-2)

Theorems & Definitions (26)

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  • ...and 16 more