Year: 2025
Type: article
Abstract: This paper explores the foundational and advanced aspects of A ∞ -algebras. We present a comprehensive study of A ∞ -algebras and their homology, emphasizing the construction of long exact sequences in simplicial homology and their implications for short exact sequences of A ∞ -algebras. Furthermore, we investigate the trace and inclusion maps in matrix A ∞ -algebras, proving their mutual invertibility and highlighting their role in preserving homological properties. These results underscore the utility of A ∞ -algebras in simplifying complex algebraic systems while maintaining essential structural invariants.
Source: Advances in Pure Mathematics
Author: Hawazin Daif Allah Alzahrani
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412586049