Strictly nilpotent elements and bispectral operators in the Weyl algebra

In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc).     

Uniform primeness of the Jordan algebra of symmetric operators

In this note we establish the best possible constant for the general lower estimate for the Jacobson - McCrimmon operator on the algebra of symmetric operators acting on a Hilbert space.

     

Multiplication operators on sobolev disk algebra

In this paper,we study the algebra consisting of analytic functions in the Sobolev space W~(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.     

Krull dimension of the enveloping algebra of a semisimple Lie algebra

Let be a complex semisimple Lie algebra and be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of is equal to the dimension of a Borel subalgebra of .

     

Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel

We show that the algebra of functions on the scheme of monic linear second-order ordinary differential operators with prescribed n + 1 regular singular points, prescribed exponents at the singular points, and having the kernel consisting of polynomials only, is isomorphic to the Bethe algebra of the Gaudin model acting on the vector space Sing of singular vectors of weight Λ^(∞) in the tensor product of finite-dimensional polynomial -modules with highest weights .      

Automorphisms of infinite dimensional Lie algebras of Cartan type

In this paper it is proved that any automorphism of an infinite dimensional Lie algebra of Cartan type over an algebraically closed field of characteristicp>2 can be induced from an automorphism of the associated divided power algebra.     

Finite Blaschke product and the multiplication operators on Sobolev disk algebra

Let R(D) be the algebra generated in Sobolev space W22(D) by the rational functions with poles outside the unit disk D. In this paper the multiplication operators Mg on R(D) is studied and it is proved that Mg ～ Mzn if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then Mg has uncountably many Banach reducing subspaces if and only if n > 1.     

q-Taylor and interpolation series for Jackson q-difference operators

We prove q-Taylor series for Jackson q-difference operators. Absolute and uniform convergence to the original function are proved for analytic functions. We derive interpolation results for entire functions of q-exponential growth which is less than lnq⁻¹, 0<q<1, from its values at the nodes , a is a non-zero complex number with absolute and uniform convergence criteria.     

Automorphisms of Incidence Algebras

We study automorphisms of the incidence algebra of a finite quasiordered set M. In particular, we describe explicitly the group of outer automorphisms and give a criterion for any automorphism of this algebra to be a product of an inner one and an automorphism of M, which corrects some results of Spiegel (2001 Spiegel , E. ( 2001 ). On the automorphisms of incidence algebras . J. Algebra 239 : 615 – 623 .[Crossref], [Web of Science ®] , [Google Scholar]).     

Automorphisms and Derivations of Certain Solvable Lie Algebras Over Commutative Rings

Let L be a finite-dimensional complex simple Lie algebra, L _? be the ?-span of a Chevalley basis of L, and L _R  = R ?_? L _? be a Chevalley algebra of type L over a commutative ring R with identity. Let ?(R) be the solvable subalgebra of L _R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ?(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ?(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ?(R) are determined.     

项链李代数的同构与同构群

研究了一些特殊箭图的同构,这些特殊箭图包括垂直叠加的箭图和水平叠加的箭图. 跟以前的研究方法相比, 文中的研究方法是不同的和新颖的, 即利用指标数组把复杂的李运算转换为多重指标集的运算.     

Congruence of selfadjoint operators

Given a bounded selfadjoint operator a in a Hilbert space , the aim of this paper is to study the orbit of a, i.e., the set of operators which are congruent to a. We establish some necessary and sufficient conditions for an operator to be in the orbit of a. Also, the orbit of a selfadjoint operator with closed range is provided with a structure of differential manifold.      

Addendum to ‘Bosonic Formulas for (k,l)-Admissible Partitions’

In our previous paper we made a combinatorial study of (k, l)-admissible partitions. This object appeared already in the work of M. Primc as a label of a basis of level k-integrable modules over . We clarify the relation between these two works. As a byproduct we obtain an explicit parameterization of the affine Weyl group of by a simple combinatorial set.     

Automorphisms of the Toeplitz algebra with piecewise continuous symbol

The automorphism group of the Toeplitz algebra generated by the Toeplitz operators, whose symbols are continuous functions on the circle beside finitely fixed points, is characterized.