TITLE:
The Morita Equivalence for the A ∞ -Algebras
AUTHORS:
Hawazin Daif Allah Alzahrani
KEYWORDS:
A-Infinity, Homology, Inclusion Map, Trace Map
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.7,
July
23,
2025
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.