Artículo
Berger, R.; Lambre, T.; Solotar, A. "Koszul calculus" (2018) Glasgow Mathematical Journal. 60(2):361-399
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Abstract:
We present a calculus that is well-adapted to homogeneous quadratic algebras. We define this calculus on Koszul cohomology - resp. homology - by cup products - resp. cap products. The Koszul homology and cohomology are interpreted in terms of derived categories. If the algebra is not Koszul, then Koszul (co)homology provides different information than Hochschild (co)homology. As an application of our calculus, the Koszul duality for Koszul cohomology algebras is proved for any quadratic algebra, and this duality is extended in some sense to Koszul homology. So, the true nature of the Koszul duality theorem is independent of any assumption on the quadratic algebra. We compute explicitly this calculus on a non-Koszul example. © Glasgow Mathematical Journal Trust 2017.
Registro:
| Documento: | Artículo |
| Título: | Koszul calculus |
| Autor: | Berger, R.; Lambre, T.; Solotar, A. |
| Filiación: | Univ Lyon, UJM-Saint-Étienne, CNRS UMR 5208, Institut Camille Jordan, Saint-Étienne, F-42023, France Laboratoire de Mathématiques Blaise Pascal, UMR 6620, CNRS, UCA, Campus Universitaire des Cézeaux, 3 place Vasarely, Aubière Cedex, 63178, France IMAS and Dto de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellòn 1, Buenos Aires, 1428, Argentina |
| Año: | 2018 |
| Volumen: | 60 |
| Número: | 2 |
| Página de inicio: | 361 |
| Página de fin: | 399 |
| DOI: | http://dx.doi.org/10.1017/S0017089517000167 |
| Título revista: | Glasgow Mathematical Journal |
| Título revista abreviado: | Glasgow. Math. J. |
| ISSN: | 00170895 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v60_n2_p361_Berger |
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Citas:
---------- APA ----------
Berger, R., Lambre, T. & Solotar, A. (2018) . Koszul calculus. Glasgow Mathematical Journal, 60(2), 361-399.http://dx.doi.org/10.1017/S0017089517000167
---------- CHICAGO ----------
Berger, R., Lambre, T., Solotar, A. "Koszul calculus" . Glasgow Mathematical Journal 60, no. 2 (2018) : 361-399.http://dx.doi.org/10.1017/S0017089517000167
---------- MLA ----------
Berger, R., Lambre, T., Solotar, A. "Koszul calculus" . Glasgow Mathematical Journal, vol. 60, no. 2, 2018, pp. 361-399.http://dx.doi.org/10.1017/S0017089517000167
---------- VANCOUVER ----------
Berger, R., Lambre, T., Solotar, A. Koszul calculus. Glasgow. Math. J. 2018;60(2):361-399.http://dx.doi.org/10.1017/S0017089517000167
