We give a complete combinatorial answer to Kostant's problem for simple highest weight
modules indexed by fully commutative permutations. We also propose a reformulation of …

It is known that the so-called monadic decomposition, applied to the adjunction connecting
the category of bialgebras to the category of vector spaces via the tensor and the primitive …

We study the existence and uniqueness of direct sum decompositions in additive
bicategories. We find a simple definition of Krull-Schmidt bicategories, for which we prove …

For a category C, D. Bourn's categories of points (categories of split epimorphisms with fixed
codomain) can be defined as categories of the form ((B, 1B)↓(C↓ B)) for some B in C. A …

We construct a new analogue of the BGG category O for the infinite-dimensional Lie
algebras g= sl (∞), o (∞), sp (∞). A main difference with the categories studied in [9] and [2] …

In this paper a left adjoint is constructed for the restriction (or pullback) functor associated to
a morphism of Lie algebras. Colimits in the category of crossed modules in Lie algebras and …

Let denote the coendomorphism left R-bialgebroid associated to a left finitely generated and
projective extension of rings R→ A with identities. We show that the category of left …

We study category O for Takiff Lie algebras g⊗ C [ϵ]/(ϵ 2) where g is the Lie algebra of a
reductive algebraic group over C. We decompose this category as a direct sum of certain …

We use Arkhipov's twisting functors to show that the universal enveloping algebra of a semi-
simple complex finite-dimensional Lie algebra surjects onto the space of ad-finite …

We study the structure of generalized Verma modules over a semi-simple complex finite-
dimensional Lie algebra, which are induced from simple modules over a parabolic …