Artículo
Kuttler, J.; Pianzola, A.; Quallbrunn, F. "Lie algebroids arising from simple group schemes" (2017) Journal of Algebra. 487:1-19
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Abstract:
A classical construction of Atiyah assigns to any (real or complex) Lie group G, manifold M and principal homogeneous G-space P over M, a Lie algebroid over M ([1]). The spirit behind our work is to put this work within an algebraic context, replace M by a scheme X and G by a “simple” reductive group scheme G over X (in the sense of Demazure–Grothendieck) that arise naturally with an attached torsor (which plays the role of P) in the study of Extended Affine Lie Algebras (see [9] for an overview). Lie algebroids in an algebraic sense were also considered by Beilinson and Bernstein. We will explain how the present work relates to theirs. © 2017 Elsevier Inc.
Registro:
| Documento: | Artículo |
| Título: | Lie algebroids arising from simple group schemes |
| Autor: | Kuttler, J.; Pianzola, A.; Quallbrunn, F. |
| Filiación: | Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada Centro de Altos Estudios en Ciencias Exactas, Avenida de Mayo 866, Buenos Aires, 1084, Argentina Departamento de matemáticas, Universidad de Buenos Aires, Argentina |
| Palabras clave: | Kähler differentials for Lie algebras; Lie algebroids; Reductive group scheme; Scheme on Lie algebras |
| Año: | 2017 |
| Volumen: | 487 |
| Página de inicio: | 1 |
| Página de fin: | 19 |
| DOI: | http://dx.doi.org/10.1016/j.jalgebra.2017.05.005 |
| Título revista: | Journal of Algebra |
| Título revista abreviado: | J. Algebra |
| ISSN: | 00218693 |
| CODEN: | JALGA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v487_n_p1_Kuttler |
Referencias:
- Atiyah, M., Complex analytic connections in fibre bundles (1957) Trans. Amer. Math. Soc., 85, pp. 181-207
- Beilinson, A., Bernstein, J., A proof of Jantzen conjectures (1993) Adv. Sov. Math., 16, pp. 1-50
- Bourbaki, N., Algèbre (1970), Chapitres 1–3 Diffusion C.C.L.S. Paris; Demazure, M., Gabriel, P., Groupes algébriques (1970), North-Holland; Grothendieck, A., Éléments de Géométrie Algébrique IV (1964) Publications mathématiques de l'I.H.E.S., 20. , (avec la collaboration de J. Dieudonné)
- Gille, P., Pianzola, A., Galois cohomology and forms of algebras over Laurent polynomial rings (2007) Math. Ann., 338, pp. 497-543
- Kuttler, J., Pianzola, A., Differentials for Lie algebras (2015) Algebr. Represent. Theory, 18 (4), pp. 941-960
- Milne, J.S., Étale Cohomology (1980), Princeton University Press; Neher, E., Extended affine Lie algebras and other generalizations of affine Lie algebras—a survey, preprint (available on Neher's homepage), 2008; Pianzola, A., Derivations of certain algebras defined by étale descent (2010) Math. Z., 264
- (1971) Séminaire de Géométrie Algébrique de l'I.H.E.S., Revêtements Étales et Groupe Fondamental, Dirigé par A. Grothendieck, Lecture Notes in Math., 224. , Springer
- (1970) Séminaire de Géométrie Algébrique de l'I.H.E.S., 1963–1964, Schémas en Groupes, Dirigé par M. Demazure et A. Grothendieck, Lecture Notes in Math., vol. 151–153. , Springer
Citas:
---------- APA ----------
Kuttler, J., Pianzola, A. & Quallbrunn, F. (2017) . Lie algebroids arising from simple group schemes. Journal of Algebra, 487, 1-19.http://dx.doi.org/10.1016/j.jalgebra.2017.05.005
---------- CHICAGO ----------
Kuttler, J., Pianzola, A., Quallbrunn, F. "Lie algebroids arising from simple group schemes" . Journal of Algebra 487 (2017) : 1-19.http://dx.doi.org/10.1016/j.jalgebra.2017.05.005
---------- MLA ----------
Kuttler, J., Pianzola, A., Quallbrunn, F. "Lie algebroids arising from simple group schemes" . Journal of Algebra, vol. 487, 2017, pp. 1-19.http://dx.doi.org/10.1016/j.jalgebra.2017.05.005
---------- VANCOUVER ----------
Kuttler, J., Pianzola, A., Quallbrunn, F. Lie algebroids arising from simple group schemes. J. Algebra. 2017;487:1-19.http://dx.doi.org/10.1016/j.jalgebra.2017.05.005
