Difference $2$-algebras and difference $A_\infty$-algebras
Year: 2026
Type: preprint
Abstract: A difference operator on an associative algebra is an algebraic abstraction of the forward and backward difference operators. In this paper, we first introduce difference operators on associative $2$-algebras and consider the category of difference associative $2$-algebras. Subsequently, we also introduce difference operators on a given $A_\infty$-algebra in terms of their Maurer-Cartan characterization. We prove that the category of difference associative $2$-algebras and the category of $2$-term difference $A_\infty$-algebras are equivalent. We characterize skeletal and strict $2$-term difference $A_\infty$-algebras by respectively third cocycles and crossed modules of difference algebras. Finally, we define the notion of a $2$-term bimodule up to homotopy over a difference algebra, which in turn yields a construction of a $2$-term difference $A_\infty$-algebra.
Source: arXiv (Cornell University)
Author: Das, Apurba
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162424337
Cites:
Cited by:
Related to: