Displaying similar documents to “The Weyl group as fixed point set of smooth involutions.”

Berezin-Weyl quantization for Cartan motion groups

Benjamin Cahen (2011)

Commentationes Mathematicae Universitatis Carolinae


We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].

Weyl Groups of Fine Gradings on Simple Lie Algebras of Types A, B, C and D

Elduque, Alberto, Kochetov, Mikhail (2012)

Serdica Mathematical Journal


2010 Mathematics Subject Classification: Primary 17B70, secondary 17B40, 16W50. 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,...

Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Liping Sun, Wende Liu (2017)

Open Mathematics


According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....