Related papers: K-Bessel functions associated to 3-rank Jordan alg…
We determine explicit orbit representatives of reducible Jordan algebras and of their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of N = 2, 4 locally…
There are Jordan analogues of annihilators in Jordan algebras which are called Jordan annihilators. The present paper is devoted to investigation of those Jordan algebras every Jordan annihilator of which is generated by an idempotent as an…
We present a method for computing the Mordell-Weil rank of the jacobian of a curve of genus 2 with multiplication by a square root of 2, based on descent via isogenies of degree 2, and apply it to a family of curves.
We classify pointed Hopf algebras with finite Gelfand-Kirillov dimension whose infinitesimal braiding has dimension 2 but is not of diagonal type, or equivalently is a block. These Hopf algebras are new and turn out to be liftings of either…
The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes…
The modified Bessel functions $K_{\nu}(z)$, or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic identities. A survey of these arithmetical identities and…
The group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.
The binomial coefficients and Catalan triangle numbers appear as weight multiplicities of the finite-dimensional simple Lie algebras and affine Kac--Moody algebras. We prove that any binomial coefficient can be written as weighted sums…
In this paper, we classify four-dimensional Jordan algebras over an algebraically closed field of characteristic different of two. We establish the list of 73 non-isomorphic Jordan algebras.
Series involving hypergeometric functions are used to derive, extend and evaluate integrals involving the product of two Bessel functions of the first kind $J_{u}(a z)$ $J_{v}(b z)$ with order $u,v$, studied by Landau et al. The method used…
The purpose of this short note is twofold: First to elucidate some connections between the ``building block'' of Dimofte--Gaiotto--Gukov's $3$D index, known as the tetrahedral index $I_\Delta (m,e)$, and Hahn--Exton's $q$-analogue of the…
In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials…
We give a classification up to equivalence of the fine group gradings by abelian groups on the Jordan pairs and triple systems of types bi-Cayley and Albert, under the assumption that the base field is algebraically closed of characteristic…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…
The paper is devoted to classify nilpotent Jordan algebras of dimension up to five over an algebraically closed field of characteristic not 2. We obtained a list of 35 isolated non-isomorphic 5-dimensional nilpotent non-associative Jordan…
We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…
We classify decompositions of simple special finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic zero into the sum of two proper simple subsuperalgebras.
In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted…
Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the mathematical mainstream were identified that fit…