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math.RT2025
Stable equivalences and homological dimensions
Xiaogang Li, Changchang Xi
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of \textbf{two} matrices. So it is fundamental to study first the centralizer al…
math.RT2025
Derived equivalences, new matrix equivalences, and homological conjectures
Xiaogang Li, Changchang Xi
Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dime…
math.RT2023
Derived and stable equivalences of centralizer matrix algebras
Xiaogang Li, Changchang Xi
The centralizer of a matrix in a full matrix algebra is called a principal centralizer matrix algebra. Characterizations are presented for principal centralizer matrix algebras to…