相关论文: A Class of Distal Functions on Semitopological Sem…
The aim of the paper is to study the ring of differential operators $\mathcal{D}(A(m))$ on the generalized multi-cusp algebra $A(m)$ where $m\in \mathbb{N}^n$ (of Krull dimension $n$). The algebra $A(m)$ is singular apart from the single…
In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and…
We consider the symmetry algebra generated by the total angular momentum operators, appearing as constants of motion of the $\mathrm{S}_3$ Dunkl Dirac equation. The latter is a deformation of the Dirac equation by means of Dunkl operators,…
We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group $G$ as their expansions into series of special functions that are invariant under the action of the even…
Building on an old result of Duncan and Namioka, we show that the ${\ell}^1$-convolution algebra of a semilattice $S$ is biflat precisely when $S$ is uniformly locally finite. The proof shows in passing that for such $S$ the convolution…
Equivariant map algebras are Lie algebras of algebraic maps from a scheme (or algebraic variety) to a target finite-dimensional Lie algebra (in the case of the current paper, we assume the latter is a simple Lie algebra) that are…
We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from…
We construct a new family of affine $W$-algebras $W^k(\lambda,\mu)$ parameterized by partitions $\lambda$ and $\mu$ associated with the centralizers of nilpotent elements in $\mathfrak{gl}_N$. The new family unifies a few known classes of…
To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…
We classify up to isomorphism all finite-dimensional Lie algebras that can be realised as Lie subalgebras of the complex Weyl algebra $A_1$. The list we obtain turns out to be discrete and for example, the only non-solvable Lie algebras…
Twisted generalized Weyl algebras (TGWAs) $A(R,\sigma,t)$ are defined over a base ring $R$ by parameters $\sigma$ and $t$, where $\sigma$ is an $n$-tuple of automorphisms, and $t$ is an $n$-tuple of elements in the center of $R$. We show…
This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…
A new descent algebra $\sum_{W}(A_{n})$ of Weyl groups of type $A_n$, constructed by present authors in [1], is generated by equivalence classes $[x_J]$ arising from the equivalence relation defined on the set of all $x_J$. In this paper,…
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept…
We introduce Nevanlinna classes of holomorphic functions associated to a closed set on the boundary of the unit disc in the complex plane and we get Blaschke type theorems relative to these classes by use of several complex variables…
To a vector space V equipped with a non-quasiclassical involutary solution of the quantum Yang-Baxter equation and a partition $\lambda$, we associate a vector space $\Vl$ and compute its dimension. The functor $V\mapsto \Vl$ is an analogue…
We investigate the representations of the hyperalgebras associated to the map algebras $\mathfrak g\otimes \mathcal A$, where $\mathfrak g$ is any finite-dimensional complex simple Lie algebra and $\mathcal A$ is any associative commutative…
This paper is intended to provide foundations to the theory of Witt-type topological group and ring functors defined on a category of topological algebras, and, in presence of Banach norms, to show how to topologically deal with them. It is…
We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse…
A fundamental construction in formal language theory is the Myhill-Nerode congruence on words, whose finitedness characterizes regular language. This construction was generalized to functions from $\Sigma^*$ to $\mathbb{Z}$ by Colcombet,…