一类推广的Virasoro-like李代数

构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.     

A Banach algebra of generalized functions

An algebraic isomorphism from a convolution algebra of Laplace transformable functions with support on the half-line to a complete discrete normed convolution algebra of sequences is used to construct generalized functions. The extension of this function-to-sequence map to a commutative Banach algebra of generalized functions is shown to be a Banach algebra isomorphism which can be utilized to establish a discrete formulation of a Mikusiński-type operational calculus and to construct algorithms for the numerical solution of half-line convolution equations.     

The first cohomology group of the generalized Morava stabilizer algebra

There exists a -local spectrum with = . Its Adams-Novikov -term is isomorphic to

where

In this paper we determine the groups

for all 0$">. Its rank ranges from to depending on the value of .

     

Subalgebras of the generalized extended galilei algebra

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 6, pp. 705–709, November–December, 1988.     

The initial algebra of maximal minors of a generalized hankel matrix

One deals with a certain generalization of the (generic) Hankel matrix. Fixing a field K, for a suitable diagonal term order on the polynomial ring B over K generated by the entries of this matrix, one considers the K-subalgebra A ? B generated by the set of initial terms of the the maximal minors of the matrix. The algebra A detects the underlying combinatorics in terms of certain generalized standard tableaux and these give a way of showing that A is normal. A more involved technique also yields that the Rees algebra of the ideal of B generated by the generators of A is normal. In particular, both algebras are Cohen-Macaulay. We also present a Gröbner basis for the presentation ideal of A and compute some numerical invariants using the simplicial complex associated to A.     

On generalized circulants over a Boolean algebra

For any given positive integer n, we give a necessary and sufficient condition for an n × nr-circulant (generalized circulant) over the Boolean algebra B = {0, 1} to be idempotent, and we present an algorith to obtain all n × n indempotent r-circulants over B for r = 0, 1,…,n ? 1.     

Derivation algebra and automorphism group of generalized topological N = 2 superconformal algebra

We determine the derivation algebra and the automorphism group of the generalized topological N = 2 superconformal algebra.     

Derivation algebra and automorphism group of generalized Ramond N = 2 superconformal algebra

In this paper, we give the definition of the generalized Ramond N = 2 superconformal algebras and discuss the derivation algebra and the automorphism group.     

Unitary representations of the generalized Virasoro current algebra

We investigate Verma modules V over the generalized Virasoro current algebrag, which is the semidirect sum of the Virasoro algebra and the central extension of a commutative algebra. It is shown that an arbitrary unitary representation with highest weight of algebrag is isomorphic to the tensor product of a unitary Fock representation ofg (or of a one-dimensional representation ofg) and a unitary representation with highest weight of the Virasoro algebra (considered as a representation of algebrag). This result is used to obtain formulas for the determinants of the matrices defining the Shapovalov form on Verma module V.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 532–538, April, 1990.     

Information system design computations using generalized matrix algebra

In the introduction a presentation is given of the design problem for information systems as one of finding and implementing the maximum difference between value and cost. Design of information systems as done to-day is very much less ambitious. The present paper is concerned with some subproblems of interest in work for designing information systems for minimum cost, which is itself only a subproblem of the total design problem.The paper presents some formalization by means of an extended matrix algebra which serves to enhance understanding of problems of information system design and to enable automatic computers to be used for design computations. This formalization is also a first step towards automatic design of information systems to prescribed specification.     

A generalized vertex operator algebra for Heisenberg intertwiners

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parameterized generalized vertex operator algebra. We illustrate some of our results with the example of integral lattice vertex operator superalgebras.     

Intrinsic definition of the Colombeau algebra of generalized functions

— G (), . . . , : , , D()G(), , , G(), , , , — .     

Full algebra of generalized functions and non-standard asymptotic analysis

We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis.     

Banach代数上的高阶Jordan-triple导子系的广义Hyers-Ulam-Rassias稳定性

针对Banach代数上的高阶Jordan—triple导子系,基于与函数方程有关的广义的Hyers—Ulam-Rassias稳定性的原理．采用线性算子论的方法,结合广义的Jensen等式,证明了Banach代数上与高阶导子系有关的函数方程具有广义的Hyers—Ulam-Rassias稳定性．证明结果表明该方法实用性强,...     

On generalized shift bases for the wiener disc algebra

LetW(D) denote the set of functionsf(z)=Σ _n=0 ^∞ A _n Z ⁿ a _nzⁿ for which Σ_n=0 ^∞|a _n |<+∞. Given any finite set lcub;f _i (z)rcub; _i=1 ⁿ inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f ₁(z)z ^kn ,f ₂(z)z ^kn+1, …,f _n (z)z ^(k+1)n−1rcub; _k=0 ^∞ is a basis forW(D) which is equivalent to the basis lcub;z ^m rcub; _m=0 ^∞ . (ii) The generalized shift sequence is complete inW(D), (iii) The function has no zero in |z|≦1, wherew=e ^2πiti /n.     

Fourier analysis on Colombeau’s algebra of generalized functions

In this paper we study Fourier transforms on Colombeau’s algebra. We present a Paley-Wiener theorem for generalized functions and introduce generalized functions with compact spectrum. When restricted to distributions this notion coincides with the classical notion of distributions of compact spectrum. We also define subalgebras where the Fourier transform is well behaved in the classical algebraic sense.