On a Construction of Representations and a Problem of Enright.
On automorphisms of Weyl algebra
On formal series and infinite products over Lie algebras.
On quasi-analytic vectors for some classes of operators
On representations of restricted Lie superalgebras
Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type , the baby Verma modules are proved to be simple for any regular nilpotent -character and typical weight . Moreover, we obtain the dimension formulas for projective covers of simple modules with -characters of standard Levi form.
On the annihilators of the simple subquotients of the principal series
On the centralizer of K in the universal enveloping algebra of SO(n,1) and SU(n,1).
On the Characterization of Primitive Ideals in Enveloping Algebras.
On the classification of primitive ideals for complex classical Lie algebras, II
On the classification of primitive ideals for complex classical Lie algebras, I
On the classification of primitive ideals for complex classical Lie algebras, III
On the double Poincaré series of the enveloping algebras of certain graded Lie algebras.
On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case
On the ghost centre of Lie superalgebras
We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.
On the Hattori-Stallings trace for certain primitive factors of enveloping algebras of semisimple Lie algebras.
On the homology of free Lie algebras
Given a principal ideal domain of characteristic zero, containing , and a connected differential non-negatively graded free finite type -module , we prove that the natural arrow is an isomorphism of graded Lie algebras over , and deduce thereby that the natural arrow is an isomorphism of graded cocommutative Hopf algebras over ; as usual, stands for free part, for homology, for free Lie algebra, and for universal enveloping algebra. Related facts and examples are also considered....
On the infinitesimal kernel of irreducible representations of nilpotent Lie groups
On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras
On the -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case
Let be a semisimple complex algebraic group and its flag variety. Let and let be its enveloping algebra. Let be a Cartan subalgebra of . For , let be the corresponding minimal primitive ideal, let , and let be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras . When is regular, Hodges has shown that . In this case is generated by the classes corresponding to...
On universal enveloping algebras in a topological setting
We study some embeddings of suitably topologized spaces of vector-valued smooth functions on topological groups, where smoothness is defined via differentiability along continuous one-parameter subgroups. As an application, we investigate the canonical correspondences between the universal enveloping algebra, the invariant local operators, and the convolution algebra of distributions supported at the unit element of any finite-dimensional Lie group, when one passes from finite-dimensional Lie groups...