自由交换Nijenhuis 代数上的左余单位Hopf代数结构

Translated title of the contribution: Left counital Hopf algebra structures on free commutative Nijenhuis algebras

Shanghua Zheng, Li Guo

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Motivated by the Hopf algebra structures established on free commutative Rota-Baxter algebras, we explore Hopf algebra related structures on free commutative Nijenhuis algebras. Applying a cocycle condition, we first prove that a free commutative Nijenhuis algebra on a left counital bialgebra (in the sense that the right-sided counicity needs not hold) can be enriched to a left counital bialgebra. We then establish a general result that a connected graded left counital bialgebra is a left counital right antipode Hopf algebra in the sense that the antipode is also only right-sided. We finally apply this result to show that the left counital bialgebra on a free commutative Nijenhuis algebra on a connected left counital bialgebra is connected and graded, hence is a left counital right antipode Hopf algebra.

Translated title of the contributionLeft counital Hopf algebra structures on free commutative Nijenhuis algebras
Original languageChinese (Traditional)
Pages (from-to)829-846
Number of pages18
JournalScientia Sinica Mathematica
Volume50
Issue number6
DOIs
StatePublished - Jun 1 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Bialgebra
  • Connected bialgebra
  • Left counital bialgebra
  • Left counital right antipode Hopf algebra
  • Nijenhuis algebra

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