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math.RA2025
Totally compatible structures on the radical of an incidence algebra
Mykola Khrypchenko
We describe totally compatible structures on the Jacobson radical of the incidence algebra of a finite poset over a field. We show that such structures are in general non-proper.
math.RA2025
Homology and cohomology of crossed products by inverse monoid actions and Steinberg algebras
Mikhailo Dokuchaev, Mykola Khrypchenko, Juan Jacobo Simón
Given a unital action of an inverse monoid on an algebra over a filed we produce (co)homology spectral sequences which converge to the Hochschild (co)homology of th…