On a homology of algebras with unit

Jacek Dębecki. "On a homology of algebras with unit." Annales Polonici Mathematici 110.2 (2014): 189-208. <http://eudml.org/doc/280956>.

@article{JacekDębecki2014,
abstract = {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.},
author = {Jacek Dębecki},
journal = {Annales Polonici Mathematici},
keywords = {homology of algebras; homology of manifolds; chain complex; de Rham complex},
language = {eng},
number = {2},
pages = {189-208},
title = {On a homology of algebras with unit},
url = {http://eudml.org/doc/280956},
volume = {110},
year = {2014},
}

TY - JOUR
AU - Jacek Dębecki
TI - On a homology of algebras with unit
JO - Annales Polonici Mathematici
PY - 2014
VL - 110
IS - 2
SP - 189
EP - 208
AB - 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.
LA - eng
KW - homology of algebras; homology of manifolds; chain complex; de Rham complex
UR - http://eudml.org/doc/280956
ER -