The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl (2, C).
The 3-state Potts model and Rogers-Ramanujan series
We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.
The adjoint representation of group algebras and enveloping algebras.
In this paper we study the Hopf adjoint action of group algebras and enveloping algebras. We are particularly concerned with determining when these representations are faithful. Delta methods allow us to reduce the problem to certain better behaved subalgebras. Nevertheless, the problem remains open in the finite group and finite-dimensional Lie algebra cases.
The algebra of compact operators does not have any finite-codimensional ideal
The approximative centre of a Lie algebra.
The arithmetic theory of loop groups
The Atiyah extension of a Lie algebra deformation.
The automorphism group of the rank 2 Lie algebra free in the variety .
The automorphisms of generalized Witt type Lie algebras.
The Azéma martingales as components of quantum independent increment processes
The bar automorphism in quantum groups and geometry of quiver representations
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.
The BGG diagram for contact orhogonal geometry of even dimension
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The Campbell-Hausdorff Formula and Invariant Hyperfunctions.
The Capelli identity, the double commutant theorem and multiplicity-free-actions.
The categories of free metabelian groups and Lie algebras
The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type .)
The center of a graded connected Lie algebra is a nice ideal
Let be a free graded connected differential Lie algebra over the field of rational numbers. An ideal in the Lie algebra is called nice if, for every cycle such that belongs to , the kernel of the map , , is contained in . We show that the center of is a nice ideal and we give in that case some informations on the structure of the Lie algebra . We apply this computation for the determination of the rational homotopy Lie algebra of a simply connected space . We deduce that the...
The center of the Dipper Donkin quantized matrix algebra.
The center of the universal enveloping algebra of a Lie algebra in characteristic