Rota–Baxter Hom-Lie–Admissible Algebras

Abstract

We study Hom-type analogs of Rota–Baxter and dendriform algebras, called Rota–Baxter G-Hom–associative algebras and Hom-dendriform algebras. Several construction results are proved. Free algebras for these objects are explicitly constructed. Various functors between these categories, as well as an adjunction between the categories of Rota–Baxter Hom-associative algebras and of Hom-(tri)dendriform algebras, are constructed.

Key Words:

• Free algebra
• Hom-associative algebra
• Hom-dendriform algebra
• Hom–Lie–admissible algebra
• Hom–Lie algebra
• Hom-preLie algebra
• Hom-tridendriform algebra
• Rota–Baxter algebra
• Rota–Baxter operator

2010 Mathematics Subject Classification:

• 16W20
• 17D25

Notes

Communicated by A. Elduque.