Isotropy subgroups of some almost rigid domains

In this paper, we describe the structure of isotropy subgroups of some almost rigid domains and give necessary and sufficient conditions for an automorphism to be an element of the isotropy subgroup.     

Diagonalization and Jordan normal form – motivation through Maple ®

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.     

Gelfand–Kirillov Dimension and Local Finiteness of Jordan Superpairs Covered by Grids and Their Associated Lie Superalgebras

Abstract

In this paper we show that a Lie superalgebra L graded by a 3-graded irreducible root system has Gelfand–Kirillov dimension equal to the Gelfand–Kirillov dimension of its coordinate superalgebra A, and that L is locally finite if and only A is so. Since these Lie superalgebras are coverings of Tits–Kantor–Koecher superalgebras of Jordan superpairs covered by a connected grid, we obtain our theorem by combining two other results. Firstly, we study the transfer of the Gelfand–Kirillov dimension and of local finiteness between these Lie superalgebras and their associated Jordan superpairs, and secondly, we prove the analogous result for Jordan superpairs: the Gelfand–Kirillov dimension of a Jordan superpair V covered by a connected grid coincides with the Gelfand– Kirillov dimension of its coordinate superalgebra A, and V is locally finite if and only if A is so.     

Dynamics, topology and bifurcations of McMullen maps

We give a survey of many diff erent topological structure arise in the dynamical and parameter planes of McMullen maps.     

Simplicity of a Vertex Operator Algebra Whose Griess Algebra is the Jordan Algebra of Symmetric Matrices

Let r ∈ ? be a complex number, and d ∈ ?_≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4 Ashihara , T. , Miyamoto , M. ( 2009 ). Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras . Journal of Algebra 32 : 1593 – 1599 . [Google Scholar]] introduced a vertex operator algebra V _𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V _𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V _𝒥 is not simple), we give a generator system of the maximal proper ideal I _r of the VOA V _𝒥 explicitly.     

Derivations of KKM Doubles

We compute derivations of Jordan superalgebras obtained from Poisson superalgebras via the Kantor–King–McCrimmon doubling process.     

The asymptotic analysis of generalized eigenvectors of some Jacobi operators. Jordan box case∗

This paper presents two methods of finding asymptotic formulae for a basis of solutions of the second order difference equations in the Jordan box case. An application to spectral analysis of Jacobi operators is also sketched.     

On a generalization of Hermite polynomials

We consider a new generalization of Hermite polynomials to the case of several variables. Our construction is based on an analysis of the generalized eigenvalue problem for the operator _∂Ax+D${\partial }_{A\mathbf{x}}+D$, acting on a linear space of polynomials of N variables, where A   is an endomorphism of the Euclidean space R^N${\mathbb{R}}^N$ and D is a second order differential operator. Our main results describe a basis for the space of Hermite–Jordan polynomials.