Geodesic
Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D
Serdica Mathematical Journal, Tome 38 (2012) no. 1-3, pp. 7-36 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

Voir la notice de l'article

Given a grading Γ : L ⨁ = g ∈ G L g on a nonassociative algebra L by an abelian group G, we have two subgroups of Aut(L): the automorphisms that stabilize each component L g (as a subspace) and the automorphisms that permute the components. By the Weyl group of Γ we mean the quotient of the latter subgroup by the former. In the case of a Cartan decomposition of a semisimple complex Lie algebra, this is the automorphism group of the root system, i.e., the so-called extended Weyl group. A grading is called fine if it cannot be refined. We compute the Weyl groups of all fine gradings on simple Lie algebras of types A, B, C and D (except D 4) over an algebraically closed field of characteristic different from 2.
Keywords: Graded Algebra, Fine Grading, Weyl Group, Simple Lie Algebra 
@article{SMJ2_2012_38_1-3_a1,
     author = {Elduque, Alberto and Kochetov, Mikhail},
     title = {Weyl {Groups} of {Fine} {Gradings} on {Simple} {Lie} {Algebras} of {Types} {A,} {B,} {C} and {D}},
     journal = {Serdica Mathematical Journal},
     pages = {7--36},
     year = {2012},
     volume = {38},
     number = {1-3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2012_38_1-3_a1/}
}
TY  - JOUR
AU  - Elduque, Alberto
AU  - Kochetov, Mikhail
TI  - Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D
JO  - Serdica Mathematical Journal
PY  - 2012
SP  - 7
EP  - 36
VL  - 38
IS  - 1-3
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2012_38_1-3_a1/
LA  - en
ID  - SMJ2_2012_38_1-3_a1
ER  - 
%0 Journal Article
%A Elduque, Alberto
%A Kochetov, Mikhail
%T Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D
%J Serdica Mathematical Journal
%D 2012
%P 7-36
%V 38
%N 1-3
%U http://geodesic.mathdoc.fr/item/SMJ2_2012_38_1-3_a1/
%G en
%F SMJ2_2012_38_1-3_a1
Elduque, Alberto; Kochetov, Mikhail. Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D. Serdica Mathematical Journal, Tome 38 (2012) no. 1-3, pp. 7-36. http://geodesic.mathdoc.fr/item/SMJ2_2012_38_1-3_a1/