Rota-type operators on null-filiform associative algebras

ABSTRACT

We give the description of homogeneous Rota–Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform associative algebras of arbitrary dimension.

KEYWORDS:

• Rota–Baxter operator
• Reynolds operator
• Nijenhuis operator
• Average operator
• differential operator
• null-filiform associative algebras

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 16W20
• 16S50

Acknowledgments

The authors would like to thank the referee for his exhaustive review of the paper as well as his suggestions which have helped to improve the work.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ivan Kaygorodov http://orcid.org/0000-0003-2084-9215

Additional information

Funding

This work was partially supported by Agencia Estatal de Investigación (Spain), grant MTM2016-79661-P (European FEDER support included, UE); Russian Foundation for Basic Research (RFBR) 17-01-00258; Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP) 17/15437-6.