Deformations and homotopy theory for Rota-Baxter family algebras
Abstrak
The concept of Rota-Baxter family algebra is a generalization of Rota-Baxter algebra. It appears naturally in the algebraic aspects of renormalizations in quantum field theory. Rota-Baxter family algebras are closely related to dendriform family algebras. In this paper, we first construct an $L_\infty$-algebra whose Maurer-Cartan elements correspond to Rota-Baxter family algebra structures. Using this characterization, we define the cohomology of a given Rota-Baxter family algebra. As an application of our cohomology, we study formal and infinitesimal deformations of a given Rota-Baxter family algebra. Next, we define the notion of a homotopy Rota-Baxter family algebra structure on a given $A_\infty$-algebra. We end this paper by considering the homotopy version of dendriform family algebras and their relations with homotopy Rota-Baxter family algebras.
Topik & Kata Kunci
Penulis (1)
Apurba Das
Akses Cepat
- Tahun Terbit
- 2022
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓