A simple note on the Yoneda (co)algebra of a monomial algebra - Université Grenoble Alpes
Article Dans Une Revue Ukrainskii Matematichniy Zhurnal Année : 2021

A simple note on the Yoneda (co)algebra of a monomial algebra

Estanislao Herscovich

Résumé

UDC 512.7 If is a monomial -algebra, it is well-known that is isomorphic to the space of (Anick) -chains for . The goal of this short note is to show that the next result follows directly from well-established theorems on -algebras, without computations: there is an -coalgebra model on satisfying that, for and , is a linear combination of , where , and . The proof follows essentially from noticing that the Merkulov procedure is compatible with an extra grading over a suitable category. By a simple argument based on a result by Keller we immediately deduce that some of these coefficients are .

Dates et versions

hal-04776882 , version 1 (12-11-2024)

Identifiants

Citer

Estanislao Herscovich. A simple note on the Yoneda (co)algebra of a monomial algebra. Ukrainskii Matematichniy Zhurnal, 2021, 73 (2), pp.275-277. ⟨10.37863/umzh.v73i2.6040⟩. ⟨hal-04776882⟩
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