Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are associative for any choice of the deformation parameters. Their Casimir operators are obtained and some of their unitary irreducible representations are constructed. For vanishing deformation, the la...

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra.

We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan’s conjecture on infinitesimal characters of Harish–Chandra modules in terms of Dirac cohomology. For our calculations we use ...

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

Abstract Using crossed homomorphisms, we show that the category of weak representations (respectively admissible representations) Lie–Rinehart algebras Leibniz pairs) is a left module over monoidal Lie algebras. In particular, corresponding bifunctor categories established to give new pairs). This generalises and unifies various existing constructions many by using this bifunctor. We construct ...

In this paper, we outline the rudiments of the representation theory of semisimple Lie algebras. We build the necessary theory in order to analyze the representations of sl2, which includes proving that representations of semisimple Lie algebras are completely reducible and preserve the Jordan decomposition. We only assume the reader has a working knowledge of linear algebra and a little famili...

In this paper we study the complete reducibility of representations of infinitedimensional Lie algebras from the perspective of representation theory of vertex algebras.