2023/02/26 by Jun Chen, Chen, Jun, Li Guo +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #18M70 12H05 18M65 12H10 16E40 16S80 18M60 #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.2302.13216
openalex publication_date 2023/02/26 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28
A differential algebra with weight is an abstraction of both the derivation (weight zero) and the forward and backward difference operators (weight ± 1). In 2010 Loday established the Koszul duality for the operad of differential algebras of weight zero. He did not treat the case of nonzero weight, noting that new techniques are needed since the operad is no longer quadratic. This paper continues Loday's work and establishes the Koszul duality in the case of nonzero weight. In the process, the minimal model and the Koszul dual homotopy cooperad of the operad governing differential algebras with weight are determined. As a consequence, a notion of homotopy differential algebras with weight is obtained and the deformation complex as well as its L_∞-algebra structure for differential algebras with weight are deduced.