Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ĝl ∞ modules of level one. Recent works have calculated these character functions for higher levels for ĝl ∞ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of h...

We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x ∈ G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite dimensional Lie algebras and some classes of infinite groups. We also consider a similar problem for pairs of elements.

2 Kac coordinates 5 2.1 Based automorphisms and affine root systems . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Torsion points, Kac coordinates and the normalization algorithm . . . . . . . . . . . . 9 2.3 μm-actions on Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Principal μm-actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove that reduced zeta functions are multiplicative under certain conditions and investigate which reduced zeta functions have functional equations.

Curvature collineations of a spray manifold induced by the Lie symmetries of the underlying spray are studied. The basic observation is that the Jacobi endomorphism and the Berwald curvature are invariant under these symmetries; this implies the invariance of the further curvature data. Our main technical tool is an appropriate Lie derivative operator along the tangent bundle projection. M.S.C....

The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept-out surface.

We study Manin triples for a reductive Lie algebra, g. First, we generalize results of E. Karolinsky, on the classification of Lagrangian subalgebras (cf. KAROLINSKY E., A Classification of Poisson homogeneous spaces of a compact Poisson Lie group, Dokl. Ak. Nauk, 359 (1998), 13-15). Then we show that, if g is non commutative, one can attach , to each Manin triple in g , another one for a stric...

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic.

In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra such that commutators of this algebra generate Lie subalgebra. It was shown that classical connection between analytic group (Lie group) and Lie algebra, proved by Lie theorems, exists between analytic loop, commutant of which is associative subloop (group), and commutant Lie algebra (an ...

Although the ideas date back to the early nineteenth century (see [1; Chapter 5] for detailed historical remarks), the theory of moving frames (“repères mobiles”) is most closely associated with the name of Élie Cartan, [12], who molded it into a powerful and algorithmic tool for studying the geometric properties of submanifolds and their invariants under the action of a transformation group. I...