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Formal deformations and principal series representations of $SL (2, ℝ)$ and $SL (2, ℂ)$

Benjamin Cahen (2020)

Czechoslovak Mathematical Journal

In this note, we study formal deformations of derived representations of the principal series representations of $SL (2, ℝ)$ . In particular, we recover all the representations of the derived principal series by deforming one of them. Similar results are also obtained for $SL (2, ℂ)$ .

Forme canonique sur le dual du fibré transverse

Tong Van Duc (1985)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Formes harmoniques et cohomologie relative des algèbres de Lie.

Annie Hersant (1983)

Journal für die reine und angewandte Mathematik

Formes harmoniques et cohomologie relative des algèbres de Lie

Annie Hersant (1985)

Bulletin de la Société Mathématique de France

Four dimensional symplectic Lie algebras.

Ovando, Gabriela (2006)

Beiträge zur Algebra und Geometrie

From Poisson algebras to Gerstenhaber algebras

Yvette Kosmann-Schwarzbach (1996)

Annales de l'institut Fourier

Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...