Derived equivalences for mirror-reflective algebras
Hongxing Chen, Changchang Xi
TL;DR
This paper proves that derived equivalences between gendo-symmetric algebras are preserved when constructing their mirror-reflective algebras, extending the understanding of derived equivalences in algebraic structures.
Contribution
It establishes that derived equivalences are inherited by mirror-reflective algebra constructions for gendo-symmetric algebras.
Findings
Mirror-reflective algebras inherit derived equivalences from their base algebras.
Derived equivalence of gendo-symmetric algebras implies derived equivalence of their mirror-reflective counterparts.
The result applies to algebras with faithful projective-injective ideals generated by idempotents.
Abstract
We show that the construction of mirror-reflective algebras inherits derived equivalences of gendo-symmetric algebras. More precisely, suppose A and B are gendo-symmetric algebras with both Ae and Bf faithful projective-injective left ideals generated by idempotents e in A and f in B, respectively. If A and B are derived equivalent, then the mirror-reflective algebras of (A,e) and (B,f) are derived equivalent.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons