Matching Rota-Baxter BiHom-algebras and related algebraic structures

DOI10.1216/rmj.2022.52.1741OpenAlexW4385640441MaRDI QIDQ2106269

Tianshui Ma, Jie Li

Publication date: 14 December 2022

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-52/issue-5/Matching-RotaBaxter-BiHom-algebras-and-related-algebraic-structures/10.1216/rmj.2022.52.1741.full

zbMATH Keywords

pre-Lie algebraspost-Lie algebrasZinbiel algebra(tri)dendriform algebrasBiHom-typeRota-Baxter associative (or Lie) algebras

Mathematics Subject Classification ID

Nonassociative algebras satisfying other identities (17A30) Hom-Lie and related algebras (17B61) Yang-Baxter equations and Rota-Baxter operators (17B38) (non-Lie) Hom algebras and topics (17D30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The category and operad of matching dialgebras
• An analytic problem whose solution follows from a simple algebraic identity
• BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras
• Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras
• Algebraic renormalisation of regularity structures
• Representations and one-parameter formal deformations of BiHom-Novikov superalgebras
• The Hopf algebras of signed permutations, of weak quasi-symmetric functions and of Malvenuto-Reutenauer
• Smash coproducts of monoidal comonads and Hom-entwining structures
• BiHom-pre-Lie algebras, BiHom-Leibniz algebras and Rota-Baxter operators on BiHom-Lie algebras
• Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras
• An algebraic study of Volterra integral equations and their operator linearity
• BiHom-alternative, BiHom-Malcev and BiHom-Jordan algebras
• Drinfeld double for infinitesimal BiHom-bialgebras
• Cotwists of bicomonads and BiHom-bialgebras
• The structure of split regular BiHom-Leibniz color algebras
• Matching Hom-setting of Rota-Baxter algebras, dendriform algebras, and pre-Lie algebras
• On unified Hom-Yetter-Drinfeld categories
• Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
• Deformations of Lie algebras using \(\sigma\)-derivations
• Hom-algebra structures
• A construction of the Hom-Yetter–Drinfeld category
• $(m, n)$-Hom-Lie algebras
• Hom-dendriform Algebras and Rota-Baxter Hom-algebras
• Universal enveloping algebras and Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras
• CUP-Product for Leibnitz Cohomology and Dual Leibniz Algebras.
• Rota–Baxter cosystems and coquasitriangular mixed bialgebras
• Coquasitriangular infinitesimal BiHom-bialgebras and related structures
• Lazy 2-cocycle and Radford (m,n)-biproduct
• Another approach to Hom-Lie bialgebras via Manin triples
• Radford (m, n)-biproduct and (m+n)-Yetter-Drinfeld category
• Quasitriangular covariant monoidal BiHom-bialgebras, associative monoidal BiHom-Yang–Baxter equations and Rota–Baxter paired monoidal BiHom-modules
• Rota–Baxter operators on BiHom-associative algebras and related structures
• Splitting of Operations, Manin Products, and Rota–Baxter Operators
• -Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation
• Pre-Poisson algebras
• On the associative analog of Lie bialgebras