The cyclic homology of
The derived join theorem and coalescence in Lie algebras
The derived Lie pseudoalgebra of an anchored module.
The Differentiable Structure of Three Remarkable Diffeomorphism Groups.
The Dixmier-Moeglin equivalence and a Gel’fand-Kirillov problem for Poisson polynomial algebras
The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only finitely many Poisson prime ideals invariant are obtained. Combined with previous work of the first-named author, this establishes the Poisson Dixmier-Moeglin equivalence for large classes of Poisson polynomial rings, including semiclassical limits of quantum matrices,...
The duality correspondence of infinitesimal characters
We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.
The dynamical quantum group.
The elliptic dynamical quantum group as an -Hopf algebroid.
The Enright Functor on the Bernstein-Gelfand-Gelfand Category ... .
The Euler-Poincaré characteristic of a Lie algebra.
The existence of c-covers of Lie algebras
The aim of this work is to obtain the structure of c-covers of c-capable Lie algebras. We also obtain some results on the existence of c-covers and, under some assumptions, we prove the absence of c-covers of Lie algebras.
The finite dimension property of the irreducible representations of Noetherian -Lie algebras.
The F-method and a branching problem for generalized Verma modules associated to
The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules.
The forms and representations of the Lie algebra .
The Frattini Argument for Lie Algebras.
The freeness of ideal subarrangements of Weyl arrangements
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers–Tymoczko. In particular, when an ideal subarrangement is equal to the entireWeyl arrangement, our...
The Frölicher-Nijenhuis bracket in non-commutative differential geometry.
The Fundamental Group of the Complement of a Union of Complex Hyperplanes.
The fundamental group of the complement of a union of complex hyperplanes: correction.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.