The Prime Spectrum of the Enveloping Algebra of a Reductive Lie Algebra.
The quantum double of a (locally) compact group.
The quantum duality principle
The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors and , inverse to...
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The representation theory of the Temperley-Lieb algebras.
The Riemann tensor for nonholonomic manifolds.
The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at .
The root space decompositions of the quadratic Lie superalgebras.
The small index property for algebras.
The socle filtration of a Verma module
The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
The spectrum of coupled random matrices.
The Steinberg Function of a Finite Lie Algebra.
The structure of complete left-symmetric algebras.
The structure of split regular Hom-Poisson algebras
We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form with U...
The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.
The structure of standard modules. II. The case A1(1), principal gradation.
The supports of simple modules over toroidal algebras.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
The tensor category of linear maps and Leibniz algebras.