Geodesic
On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 384-390

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

In the paper, the connection between algebraic and topological properties of compact semisimple Lie groups is studied. Three series of examples of compact semisimple Lie groups are given which are not isomorphic to each other but are diffeomorphic.
Mots-clés : compact Lie group, simple compact Lie group
Keywords: semisimple compact Lie group, locally isomorphic Lie groups, homotopy groups, cohomology algebra. 
V. V. Gorbatsevich. On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups. Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 384-390. http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a6/
@article{MZM_2022_112_3_a6,
     author = {V. V. Gorbatsevich},
     title = {On the {Isomorphism} and {Diffeomorphism} of {Compact} {Semisimple} {Lie} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {384--390},
     year = {2022},
     volume = {112},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a6/}
}
TY  - JOUR
AU  - V. V. Gorbatsevich
TI  - On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups
JO  - Matematičeskie zametki
PY  - 2022
SP  - 384
EP  - 390
VL  - 112
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a6/
LA  - ru
ID  - MZM_2022_112_3_a6
ER  - 
%0 Journal Article
%A V. V. Gorbatsevich
%T On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups
%J Matematičeskie zametki
%D 2022
%P 384-390
%V 112
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a6/
%G ru
%F MZM_2022_112_3_a6

[1] E. B. Vinberg, V. V. Gorbatsevich, A. L. Onischik, “Stroenie grupp i algebr Li”, Gruppy Li i algebry Li – 3, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 41, VINITI, M., 1990, 5–253 | MR | Zbl

[2] A. T. Fomenko, D. B. Fuks, Kurs gomotopicheskoi topologii, Nauka, M., 1989 | MR

[3] A. Khatcher, Algebraicheskaya topologiya, MTsNMO, M., 2011

[4] M. Mimura, H. Toda, Topology of Lie Groups. I, II, Amer. Math. Soc., Providence, RI, 1991 | MR

[5] V. L. Popov, Underlying Varieties and Group Structures, 2021, arXiv: 2105.12861.v1

[6] H. Toda, “A note on compact semi-simple Lie groups”, Japan. J. Math., 2:2 (1976), 355–358 | DOI | MR

[7] H. Scheerer, “Homotopieaquivalente compacte Liesche gruppen”, Topology, 7 (1968), 227–232 | DOI | MR

[8] S. Boekholt, “Compact Lie groups with isomorphic homotopy groups”, J. Lie Theory, 8 (1988), 183–185 | MR

[9] F. Notbohm, “On the “classifying space” functor for compact Lie groups”, J. London Math. Soc. (2), 52 (1995), 185–198 | DOI | MR

[10] P. Baum, W. Browder, “The cohomology of quotiens of classical groups”, Topology, 3 (1965), 305–336 | DOI | MR

[11] V. V. Gorbatsevich, “On some cohomology invariants of compact homogeneous spaces”, Lie Groups, Their Discrete Subgroups, and Invariant Theory, Adv. Soviet Math., 8, Amer. Math. Soc., Providence, RI, 1992, 69–85 | MR