Twisted dendriform algebras and the pre-Lie Magnus expansion

Abstract

In this paper an application of the recently introduced pre-Lie Magnus expansion to Jackson's q-integral and q-exponentials is presented. Twisted dendriform algebras, which are the natural algebraic framework for Jackson's q-analogues, are introduced for that purpose. It is shown how the pre-Lie Magnus expansion is used to solve linear q-differential equations. We also briefly outline the theory of linear equations in twisted dendriform algebras.

improved version; accepted for publication in the Journal of Pure & Applied Algebra

References in corpus (4)

• The Magnus expansion and some of its applications
• On Products and Duality of Binary, Quadratic, Regular Operads
• A Magnus- and Fer-type formula in dendriform algebras
• A rooted-trees q-series lifting a one-parameter family of Lie idempotents

Cited by in corpus (5)

• On algebraic structures of numerical integration on vector spaces and manifolds
• Rota-Baxter operators on BiHom-associative algebras and related structures
• Rota-Baxter Operators on pre-Lie superalgebras and beyond
• The tridendriform structure of a Magnus expansion
• {sigma, tau}-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation