On a homology of algebras with unit

• Autorzy: Jacek Dębecki
• Języki publikacji: EN

Abstrakty

EN

We present a very general construction of a chain complex for an arbitrary (even non-associative and non-commutative) algebra with unit and with any topology over a field with a suitable topology. We prove that for the algebra of smooth functions on a smooth manifold with the weak topology the homology vector spaces of this chain complex coincide with the classical singular homology groups of the manifold with real coefficients. We also show that for an associative and commutative algebra with unit endowed with the discrete topology this chain complex is dual to the de Rham complex.

Kategorie tematyczne

• 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, Andr\'e-Quillen, cyclic, dihedral, etc.)
• 55N35: Other homology theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 110
• Numer: 2
• Strony: 189-208

Daty

wydano

2014

Twórcy

autor

Jacek Dębecki

• Instytut Matematyki Uniwersytetu Jagiellońskiego, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap110-2-6