Twisted pre-Lie algebras of finite topological spaces

Abstract

In this paper, we first study the species of finite topological spaces recently considered by Fauvet, Foissy, and Manchon. Then, we construct a twisted pre-Lie structure on the species of connected finite topological spaces. The underlying pre-Lie structure defines a coproduct on the species of finite topological spaces different from those already defined by the authors above. In the end, we illustrate the link between the Grossman–Larson product and the proposed coproduct.

Keywords:

• Bialgebras
• bimonoids
• finite topological spaces
• Hopf algebras
• species

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16T05
• 16T10
• 16T15
• 16T30
• 06A11

Acknowledgments

I would like to thank my Ph.D. thesis supervisors: Professor Dominique Manchon and Professor Ali Baklouti for their advice, guidance and constant support.

Additional information

Funding

This work was supported by the University of Sfax, Tunisia.