相关论文: Selberg Type Integrals Associated with $sl_3$
Three kinds of universal central extension are considered for a perfect Lie algebra. More precisely, one can consider such a Lie algebra as a Lie triple system, or a Leibniz algebra and construct appropriate central extensions. We show that…
We exhibit three classes of algebraic constraints which are shown compatible with Volterra lattice.
This paper introduces and investigates the structure of $\delta$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $\delta$. The authors define $\delta$-Lie algebras, $\delta$-Lie…
We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over C, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on N-graded Lie algebras of…
We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups…
We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic…
We show a degree formula for a type of orthogonal Deligne--Lusztig varieties and their Pl\"ucker embeddings. This is an analog of work of Li on a unitary case.
The symplectic structures on $3$-Lie algebras and metric symplectic $3$-Lie algebras are studied. For arbitrary $3$-Lie algebra $L$, infinite many metric symplectic $3$-Lie algebras are constructed. It is proved that a metric $3$-Lie…
In this paper, we will present Brauer algebras associated to spherical Coxeter groups of type H3 and H4, which are also can be regarded as subalgebras of Brauer algebras D6 and E8 by Muhlherr's admissible partition. Also some basic…
We have derived a family of equations related to the untwisted affine Lie algebras $A^{(1)}_{r}$ using a Coxeter $\mathbb{Z}_{r+1}$ reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. We…
A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the…
In this paper, we prove a discrete analog of the Selberg Trace Formula for the group $\text{GL}_{3}(\mathbb{F}_q).$ By considering a cubic extension of the finite field $\mathbb{F}_q$, we define an analog of the upper half space and an…
We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of…
A method based on the quantum Calogero-Sutherland model is used to obtain generating functions for characters and multiplicities of $A_3$. Some comments on other rank three algebras are offered.
The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. We introduce a more general form…
Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…
A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral…
In the present paper, we define the Terwilliger algebra of digraphs. Then, we determine the irreducible modules of the Terwilliger algebra of a Hamming digraph $H^*(d,3)$. As is well known, the representation of the Terwilliger algebra of a…
Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.
We present coalgebras of some classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3-order symmetric group. Amongst these algebras we find the well-known Vinberg algebras, the…