Geodesic
Lie groups with commuting and anticommuting parameters
Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 311-325 
F. A. Berezin; G. I. Kats. Lie groups with commuting and anticommuting parameters. Sbornik. Mathematics, Tome 11 (1970) no. 3, pp. 311-325. http://geodesic.mathdoc.fr/item/SM_1970_11_3_a1/
@article{SM_1970_11_3_a1,
     author = {F. A. Berezin and G. I. Kats},
     title = {Lie groups with commuting and anticommuting parameters},
     journal = {Sbornik. Mathematics},
     pages = {311--325},
     year = {1970},
     volume = {11},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_11_3_a1/}
}
TY  - JOUR
AU  - F. A. Berezin
AU  - G. I. Kats
TI  - Lie groups with commuting and anticommuting parameters
JO  - Sbornik. Mathematics
PY  - 1970
SP  - 311
EP  - 325
VL  - 11
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1970_11_3_a1/
LA  - en
ID  - SM_1970_11_3_a1
ER  - 
%0 Journal Article
%A F. A. Berezin
%A G. I. Kats
%T Lie groups with commuting and anticommuting parameters
%J Sbornik. Mathematics
%D 1970
%P 311-325
%V 11
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1970_11_3_a1/
%G en
%F SM_1970_11_3_a1

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

In this paper we study analogs of Lie algebras and formal Lie groups. These analogs of groups differ from usual Lie groups, roughly speaking, in that they admit anticommuting canonical parameters. The analogs of Lie algebras differ from usual Lie algebras by properties of the commutator. In the definition of these objects an essential role is played by the gradient. In case it is trivial they become Lie groups and algebras in the usual sense. To these generalized objects we carry over classical theorems on the connection between Lie groups and algebras and the basic representation theory. Bibliography: 11 titles.

[1] W. Milnor, I. C. Moore, “On the structure of Hopf algebras”, Ans. Math., 81:2 (1965), 211–264 | DOI | MR | Zbl

[2] A. Grothendieck, “Elements de Geométrie algébrique. III”, Inst. Haute Etudes Sci., 11 (1961)

[3] Yu. I. Manin, “Teoriya kommutativnykh formalnykh grupp nad polyami konechnoi kharakteristiki”, Uspekhi matem. nauk, XVIII:6(114) (1963), 3–90 | MR

[4] L. S. Pontryagin, Topologicheskie gruppy, Gostekhizdat, Moskva, 1954

[5] F. A. Berezin, F. I. Karpelevich, “Algebry Li s dopolnitelnoi strukturoi”, Matem. sb., 77(119) (1968), 201–221 | MR | Zbl

[6] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, Moskva, 1965 | MR

[7] S. Maklein, Gomologiya, Mir, Moskva, 1966

[8] S. Bochner, “Formal Lie Groups”, Ann. Math., 47:2 (1946), 192–212 | DOI | MR

[9] E. B. Dynkin, “Normirovannye algebry Li i analiticheskie gruppy”, Uspekhi matem. nauk, V (1950), 135–186 | MR

[10] F. A. Berezin, “Avtomorfizmy grassmanovoi algebry”, Matem. zametki, 1:3 (1967), 269–276 | MR | Zbl

[11] M. Lazard, “Lois de Groupes et Analyseurs”, Ann. Scient. École Norm. Supér., LXXII (1955), 299–400 | MR