A notion of generalized highest weight modules over the high rank Virasoro algebras is introduced in this paper, and a theorem, which was originally given as a conjecture by Kac over the Virasoro algebra, is generalized. Mainly, we prove that a simple Harish-Chandra module over a high rank Virasoro algebra is either a generalized highest weight module, or a module of the intermediate series.

using fixed point method, we prove some new stability results for lie $(alpha,beta,gamma)$-derivations and lie $c^{ast}$-algebra homomorphisms on lie $c^{ast}$-algebras associated with the euler-lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

Let (S,≤) be a strictly totally ordered monoid, R be a commutative ring and M be an R-module. We show the following results: (1) If (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a semi Hopfian [[RS,≤]]-module if and only if M is a semi Hopfian R-module; (2) If (S,≤) is artinian, then the generalized inverse polynomial module [MS,...

Let V be Euclidean space. Let W ⊂ GL(V ) be a finite irreducible reflection group. Let A be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H ∈ A choose αH ∈ V ∗ such that H = ker(αH). The arrangement A is known to be free: the derivation module D(A) = {θ ∈ DerS | θ(αH ) ∈ SαH} is a free S-module with generators of degrees equal to the exponents of ...

Abstract The system presented in this paper is concerned with the computational processing of the selected types of Czech word-formation. The developed programming tool (word-formation module) aims at analysing and synthesising Czech derived words. Such a system is of particular value for automatic processing of Czech language where derivational morphology plays an important role in regular wor...

We introduce a notion of strongly C×-graded, or equivalently, C/Zgraded generalized g-twisted V -module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V -module if V admits an additional C-grading compatible with g. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0)...

Due to the special requirements of distributed systems, it is important that modeling techniques for this kind of systems ooer a stringent module concept. Each module has to support the encapsulation of data structure as well as functionality also at runtime. Modular graph transformation, presented in this contribution, supports these features. Modules are built up of speciications where attrib...

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...