Borel Subgroups of Cremona Groups
Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 72-80.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the affine-triangular subgroups are Borel subgroups of Cremona groups.
Keywords: the Cremona group, triangular subgroup, affine-triangular subgroup, the Borel subgroup.
@article{MZM_2017_102_1_a7,
     author = {V. L. Popov},
     title = {Borel {Subgroups} of {Cremona} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {72--80},
     publisher = {mathdoc},
     volume = {102},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a7/}
}
TY  - JOUR
AU  - V. L. Popov
TI  - Borel Subgroups of Cremona Groups
JO  - Matematičeskie zametki
PY  - 2017
SP  - 72
EP  - 80
VL  - 102
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a7/
LA  - ru
ID  - MZM_2017_102_1_a7
ER  - 
%0 Journal Article
%A V. L. Popov
%T Borel Subgroups of Cremona Groups
%J Matematičeskie zametki
%D 2017
%P 72-80
%V 102
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a7/
%G ru
%F MZM_2017_102_1_a7
V. L. Popov. Borel Subgroups of Cremona Groups. Matematičeskie zametki, Tome 102 (2017) no. 1, pp. 72-80. http://geodesic.mathdoc.fr/item/MZM_2017_102_1_a7/

[1] J.-P. Serre, “Le groupe de Cremona et ses sous-groupes finis”, Astérisque, 332 (2010), 75–100 | MR | Zbl

[2] J. Blanc, “Groupes de Cremona, connexité et simplicité”, Ann. Sci. Éc. Norm. Supér. (4), 43:2 (2010), 357–364 | MR | Zbl

[3] J. Blanc, J.-P. Furter, “Topologies and structures of the Cremona groups”, Ann. of Math. (2), 178:3 (2013), 1173–1198 | DOI | MR | Zbl

[4] C. P. Ramanujam, “A note on automorphism groups of algebraic varieties”, Math. Ann., 156 (1964), 25–33 | DOI | MR | Zbl

[5] V. L. Popov, “On infinite dimensional algebraic transformation groups”, Transform. Groups, 19:2 (2014), 549–568 | DOI | MR | Zbl

[6] M. Demazure, “Topologies and structures of the Cremona groups”, Ann. Sci. École Norm. Supér. (4), 3 (1970), 507–588 | MR | Zbl

[7] V. L. Popov, “Some subgroups of the Cremona groups”, Affine Algebraic Geometry, World Sci. Publ., Singapore, 2013, 213–242 | MR | Zbl

[8] V. L. Popov, “Tory v gruppakh Kremony”, Izv. RAN. Ser. matem., 77:4 (2013), 103–134 | DOI | MR | Zbl

[9] J.-P. Furter, P.-M. Poloni, On the Maximality of the Triangular Subgroup, 2016, arXiv: 1605.06344

[10] B. L. van der Varden, Algebra, Nauka, M., 1976 | MR

[11] D. A. Suprunenko, Gruppy matrits, Nauka, M., 1972 | MR | Zbl

[12] S. Akbari, R. Ebrahimian, H. Momenaee Kermani, A. Salehi Golsefidy, “Maximal subgroups of $\mathrm{GL}_n(D)$”, J. Algebra, 259:1 (2003), 201–225 | DOI | MR | Zbl

[13] A. Borel, Linear Algebraic Groups, Grad. Texts in Math., 126, Springer-Verlag, New York, 1991 | MR | Zbl

[14] J. E. Humphreys, Linear Algebraic Groups, Grad. Texts in Math., 21, Springer-Verlag, New York, 1975 | MR | Zbl

[15] T. A. Springer, Linear Algebrac Groups, Progr. Math., 9, Birkhäuser Boston, Boston, MA, 1998 | MR | Zbl

[16] Y. Berest, A. Eshmatov, F. Eshmatov, “Dixmier groups and Borel subgroups”, Adv. Math., 286 (2016), 387–429 | DOI | MR | Zbl

[17] V. L. Popov, “On actions of $\mathbf G_a$ on $\mathbf A^n$”, Algebraic Groups, Lecture Notes in Math., 1271, Springer-Verlag, Berlin, 1987, 237–242 | DOI | MR | Zbl