Geodesic
On a homology of algebras with unit
Jacek Dębecki1
1 Instytut Matematyki Uniwersytetu Jagiellońskiego Łojasiewicza 6 30-348 Kraków, Poland
Annales Polonici Mathematici, Tome 110 (2014) no. 2, pp. 189-208.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap110-2-6
Keywords: present general construction chain complex arbitrary even non associative non commutative algebra unit topology field suitable topology prove algebra smooth functions smooth manifold weak topology homology vector spaces chain complex coincide classical singular homology groups manifold real coefficients associative commutative algebra unit endowed discrete topology chain complex dual rham complex

Jacek Dębecki 1

1 Instytut Matematyki Uniwersytetu Jagiellońskiego Łojasiewicza 6 30-348 Kraków, Poland 
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Jacek Dębecki. On a homology of algebras with unit. Annales Polonici Mathematici, Tome 110 (2014) no. 2, pp. 189-208. doi : 10.4064/ap110-2-6. http://geodesic.mathdoc.fr/articles/10.4064/ap110-2-6/

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