Modified Rota–Baxter Algebras, Shuffle Products and Hopf Algebras

Xigou Zhang, Xing Gao, Li Guo

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we begin a systematic study of modified Rota–Baxter algebras, as an associative analogue of the modified classical Yang–Baxter equation. We construct free commutative modified Rota–Baxter algebras by a variation of the shuffle product and describe the structure both recursively and explicitly. We then provide these algebras with a Hopf algebra structure by applying a Hochschild cocycle.

Original languageEnglish (US)
Pages (from-to)3047-3072
Number of pages26
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume42
Issue number6
DOIs
StatePublished - Nov 15 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Bialgebra
  • Hopf algebra
  • Modified Rota–Baxter algebra
  • Rota–Baxter algebra
  • Shuffle product

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