Matrix Integrals, Toda Symmetries, Virasoro Constraints and Orthogonal Polynomials
Matrix representations for low dimensional Lie algebras.
Maximal ideals in the Lie algebra of vector fields
Maximal solvable extensions of filiform algebras
It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result.
Measured quantum groupoids associated with matched pairs of locally compact groupoids
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.
Mémoire de Bertram Kostant sur les applications de la cohomologie des algèbres de Lie réductives
Minimal realizations of classical simple Lie algebras through deformations
Minimally nonassociative Moufang loops with a unique nonidentity commutator are ring alternative
We investigate finite Moufang loops with a unique nonidentity commutator which are not associative, but all of whose proper subloops are associative. Curiously, perhaps, such loops turn out to be ``ring alternative'', in the sense that their loop rings are alternative rings.
Miura opers and critical points of master functions
Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...
Möbius inversion for the Bruhat ordering on a Weyl group
Modèle de Whittaker et ideaux primitifs complètement premiers dans les algèbres enveloppantes des algèbres de Lie semisimples complexes II.
Modèles minimaux pour les algèbres de chaines
Models of quadratic algebras generated by superintegrable systems in 2D.
Models of representations of some classical supergroups.
Modular annihilator Jordan pairs.
Modular Bernstein algebras.
Modular classes of Q-manifolds: a review and some applications
A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including -algebroids and higher Poisson manifolds.
Modular Classes of Q-Manifolds, Part II: Riemannian Structures Odd Killing Vectors Fields
We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.
Modular Forms and Root Systems.
Modular vector fields and Batalin-Vilkovisky algebras
We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the Gerstenhaber...