The Algebraic and Geometric Classification of Nilpotent Assosymmetric Algebras

Abstract

We present algebraic and geometric classifications of the 4-dimensional complex nilpotent assosymmetric algebras.

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Acknowledgments

This work was supported by FAPESP 18/15712-0; RFBR 18-31-20004; AP05131123 ”Cohomological and structural problems of non-associative algebras”. The authors thank Prof. Dr. Mykola Khrypchenko for constructive discussions about degenerations of algebras.

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Correspondence to Ivan Kaygorodov.

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Presented by: Michel Brion

Appendix

Appendix

Table 1 The list of 4-dimensional nilpotent “pure” assosymmetric algebras
Table 2 The list of 4-dimensional nilpotent “pure” assosymmetric algebras

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Ismailov, N., Kaygorodov, I. & Mashurov, F. The Algebraic and Geometric Classification of Nilpotent Assosymmetric Algebras. Algebr Represent Theor 24, 135–148 (2021). https://doi.org/10.1007/s10468-019-09935-y

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Keywords

  • Assosymmetric algebras
  • Nilpotent algebras
  • Algebraic classification
  • Central extension
  • Geometric classification
  • Degeneration

Mathematics Subject Classification 2010

  • 17A30
  • 17D25
  • 14D06
  • 14L30