On the Chevalley restriction theorem.
On the classification of -dimensional -manifold algebras
-manifold algebras are focused on the algebraic properties of the tangent sheaf of -manifolds. The local classification of 3-dimensional -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional -manifold algebras over the complex field .
On the classification of 3-dimensional coloured Lie algebras
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.
On the classification of 3-dimensional non-associative division algebras over -adic fields
Let be a prime and a -adic field (a finite extension of the field of -adic numbers ). We employ the main results in [12] and the arithmetic of elliptic curves over to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over to the classification of ternary cubic forms over (up to equivalence) with no non-trivial zeros over . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...
On the classification of Moore algebras and their deformations.
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 classification of the Lie algebras .
On the classification of the real flexible division algebras
We investigate the class of finite-dimensional real flexible division algebras. We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras to the normal...
On the cohomology of nilpotent Lie algebras
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the combinatorial Kashiwara-Vergne conjecture. (Sur la conjecture combinatoire de Kashiwara-Vergne.)
On the combinatorics of Kac's asymmetry function
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
On the combinatorics of Young-Capelli symmetrizers.
On the complicatedness of the pair (g,K).
On the composition structure of the twisted Verma modules for
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
On the computation of Clebsch-Gordan coefficients and the dilation effect.
On the constructions of Tits and Faulkner: an isomorphism theorem.
On the CR-structure of certain linear group orbits in infinite dimensions
For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits explicitly and show as main result that every continuous CR-function on has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite...