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pro vyhledávání: '"Millès, Joan"'
Autor:
Bellier-Millès, Joan, Yalin, Sinan
The Andr\'e-Quillen cohomology of an algebra with coefficients in a module is defined by deriving a functor based on K\"ahler differential forms. It can be computed using a cofibrant resolution of the algebra in a model category structure where weak
Externí odkaz:
http://arxiv.org/abs/2401.14309
Autor:
Hirsh, Joseph, Millès, Joan
In this corrigendum, we explain and correct a mistake in our article ''Curved Koszul duality theory''. Our definitions of morphisms between semi-augmented properads and between curved coproperads have to be modified.
Comment: Mathematische Annal
Comment: Mathematische Annal
Externí odkaz:
http://arxiv.org/abs/2311.05631
Curved algebras are algebras endowed with a predifferential, which is an endomorphism of degree -1 whose square is not necessarily 0. This makes the usual definition of quasi-isomorphism meaningless and therefore the homotopical study of curved algeb
Externí odkaz:
http://arxiv.org/abs/2007.03004
In 2007, Vallette built a bridge across posets and operads by proving that an operad is Koszul if and only if the associated partition posets are Cohen-Macaulay. Both notions of being Koszul and being Cohen-Macaulay admit different refinements: our g
Externí odkaz:
http://arxiv.org/abs/1811.11770
Autor:
Millès, Joan
Nous explicitons la cohomologie d'André-Quillen des algèbres sur une opérade à l'aide de la dualité de Koszul des opérades. Cette cohomologie est représentée par le complexe cotangent. Nous donnons des critères assurant que cette cohomologie
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00551947
http://tel.archives-ouvertes.fr/docs/00/55/19/47/PDF/these.pdf
http://tel.archives-ouvertes.fr/docs/00/55/19/47/PDF/these.pdf
Autor:
Millès, Joan
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex structure o
Externí odkaz:
http://arxiv.org/abs/1409.3604
Autor:
Hirsh, Joseph, Millès, Joan
We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the category of
Externí odkaz:
http://arxiv.org/abs/1008.5368
Autor:
Milles, Joan
We extend the Koszul duality theory of associative algebras to algebras over an operad. Recall that in the classical case, this Koszul duality theory relies on an important chain complex: the Koszul complex. We show that the cotangent complex, involv
Externí odkaz:
http://arxiv.org/abs/1004.0096
Autor:
Hirsh, Joseph, Millès, Joan
Publikováno v:
Mathematische Annalen; May2024, Vol. 389 Issue 1, p999-1005, 7p
Autor:
Millès, Joan
Publikováno v:
Adv. Math. 226 (2011), pp. 5120-5164
We study the Andr\'e-Quillen cohomology with coefficients of an algebra over an operad. Using resolutions of algebras coming from Koszul duality theory, we make this cohomology theory explicit and we give a Lie theoretic interpretation. For which ope
Externí odkaz:
http://arxiv.org/abs/0806.4405