2017/04/17 by Wei Hu, Hu, Wei, Changchang Xi +1 · 1 citation
Mathematics · Physics and Astronomy · #16G10 #16S10 #18E30 #18G15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1704.04914
openalex publication_date 2017/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Derived equivalences for Artin algebras (and almost ν-stable derived equivalences for finite-dimensional algebras) are constructed from Milnor squares of algebras. Particularly, three operations of gluing vertices, unifying arrows and identifying socle elements on derived equivalent algebras are presented to produce new derived equivalences of the resulting algebras from the given ones. As a byproduct, we construct a series of derived equivalences, showing that derived equivalences may change Frobenius type of algebras in general, though both tilting procedure and almost ν-stable derived equivalences do preserve Frobenius type of algebras.