On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
On the unitarizability of derived functor modules.
On the vanishing of extensions of modules over reduced enveloping algebras.
On the variety of 3-dimensional Lie algebras.
On the variety of lagrangian subalgebras, I
On the variety of lagrangian subalgebras, II
On the zeros of polynomials over arbitrary finite dimensional algebras.
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
On unitary convex decompositions of vectors in a -algebra
By exploiting his recent results, the author further investigates the extent to which variation in the coefficients of a unitary convex decomposition of a vector in a unital -algebra permits the vector decomposable as convex combination of fewer unitaries; certain -algebra results due to M. Rørdam have been extended to the general setting of -algebras.
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...
On Whitehead's second lemma for Lie algebras.
On Whittaker Vectors and Representation Theory.
On Witten multiple zeta-functions associated with semisimple Lie algebras I
We define Witten multiple zeta-functions associated with semisimple Lie algebras , of several complex variables, and prove the analytic continuation of them. These can be regarded as several variable generalizations of Witten zeta-functions defined by Zagier. In the case , we determine the singularities of this function. Furthermore we prove certain functional relations among this function, the Mordell-Tornheim double zeta-functions and the Riemann zeta-function. Using these relations, we prove...
One-dimensional infinitesimal-birational duality through differential operators
The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.
One-dimensional subalgebras of a Bernstein algebra.
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
One-parameter contractions of Lie-Poisson brackets
We consider contractions of Lie and Poisson algebras and the behaviour of their centres under contractions. A polynomial Poisson algebra is said to be of Kostant type, if its centre is freely generated by homogeneous polynomials such that they give Kostant’s regularity criterion on are linear independent if and only if the Poisson tensor has the maximal rank at ). If the initial Poisson algebra is of Kostant type and satisfy a certain degree-equality, then the contraction is also of Kostant...
One-parameter subgroups and the B-C-H formula
An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the associated...
One-sided division absolute valued algebras.
We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...
Opérades différentielles graduées sur les simplexes et les permutoèdres
On définit plusieurs opérades différentielles graduées, dont certaines en relation avec des familles de polytopes : les simplexes et les permutoèdres. On obtient également une présentation de l’opérade liée aux associaèdres introduite dans un article antérieur.