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The algebraic classification of nilpotent Novikov algebras

Kobiljon Abdurasulov, Ivan Kaygorodov, Abror Khudoyberdiyev

Abstract

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.

The algebraic classification of nilpotent Novikov algebras

Abstract

This paper is devoted to the complete algebraic classification of complex -dimensional nilpotent Novikov algebras.
Paper Structure (31 sections, 2 theorems, 53 equations)

This paper contains 31 sections, 2 theorems, 53 equations.

Table of Contents

  1. The algebraic classification of nilpotent Novikov algebras
  2. Method of classification of nilpotent algebras
  3. Notations
  4. $1$-dimensional central extensions of $4$-dimensional $2$-step nilpotent Novikov algebras
  5. The description of second cohomology space
  6. Central extensions of ${\mathfrak N}_{01}$
  7. Central extensions of ${\mathfrak N}_{02}$
  8. Central extensions of ${\mathfrak N}_{04}^0$
  9. Central extensions of ${\mathfrak N}_{07}$
  10. Central extensions of ${\mathfrak N}_{08}^{\alpha\neq1}$
  11. Central extensions of ${\mathfrak N}_{08}^{1}$
  12. Central extensions of ${\mathfrak N}_{12}$
  13. Central extensions of ${\mathfrak N}_{13}$
  14. Central extensions of ${\mathfrak N}_{14}^0$
  15. Central extensions of ${\mathfrak N}_{14}^1$
  16. ...and 16 more sections

Key Result

Lemma 1

Let ${\bf A}$ be an $n$-dimensional Novikov algebra such that $\dim (\operatorname{Ann}({\bf A}))=m\neq0$. Then there exists, up to isomorphism, a unique $(n-m)$-dimensional Novikov algebra ${\bf A}'$ and a bilinear map $\theta \in {\rm Z^2}({\bf A}, {\mathbb V})$ with $\operatorname{Ann}({\bf A})\c

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Definition 2
  • Definition 3
  • Lemma 4