相关论文: Ideals in the center of symmetric algebras
Ideals are one of the main topics of interest to the study of the order structure of an algebra. Due to their nice properties, ideals have an important role both in lattice theory and semigroup theory. Two natural concepts of ideal can be…
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…
We describe the Poisson ideals and attached symplectic geometry of a cluster algebra with compatible Poisson structure. We apply these results to determine the spectrum of a quantum cluster algebra. As an application, we describe the…
There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the…
We consider when the symmetric algebra of an infinite-dimensional Lie algebra, equipped with the natural Poisson bracket, satisfies the ascending chain condition (ACC) on Poisson ideals. We define a combinatorial condition on a graded Lie…
The paper contributes to the structure theory of primitive axial algebras. For a primitive axial algebra $A$ with a Frobenius form we compare the largest ideal $R(A)$ not containing any of the generating axes, the radical $A^\perp$ of the…
In this paper we show that the center of the partition algebra $\mathcal{A}_{2k}(\delta)$, in the semisimple case, is given by the subalgebra of supersymmetric polynomials in the normalised Jucys-Murphy elements. For the non-semisimple…
Let $\mathcal{A}$ denote a central hyperplane arrangement of rank $n$ in affine space $\mathbb{K}^n$ over an infinite field $\mathbb{K}$ and let $l_1,\ldots, l_m\in R:= \mathbb K[x_1,\ldots,x_n]$ denote the linear forms defining the…
We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the…
In this paper, we investigate some topics around the closed image $S$ of a rational map $\lambda$ given by some homogeneous elements $f_1,...,f_n$ of the same degree in a graded algebra $A$. We first compute the degree of this closed image…
A symmetric ideal is an ideal in a polynomial ring which is stable under all permutations of the variables. In this paper we initiate a global study of zero-dimensional symmetric ideals. By this we mean a geometric study of the invariant…
We describe the Jacobson topology of the primitive ideal space of self-similar k-graph C*-algebras under certain conditions.
We determine all the ideals of the homological Goldman Lie algebra, which reflects the structure of an oriented surface.
We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit space of the groupoid. We apply this to obtain results about…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
In this paper, we study the structure of closed algebraic ideals in the algebra of operators acting on a Lorentz sequence space.
We describe the primitive ideal spaces and the Jacobson topologies of a special class of topological graph algebras.
The algebra in the title has been introduced by P. Aluffi. Let $J\subset I$ be ideals in the commutative ring $R$. The (embedded) Aluffi algebra of $I$ on $R/J$ is an intermediate graded algebra between the symmetric algebra and Rees…
A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…
We obtain a complete description of closed ideals of the algebra $\mathcal{D}\cap \mathrm{lip}_\alpha},$ $0<\alpha\leq{1/2},$ where $\mathcal{D}$ is the Dirichlet space and $\mathrm{lip}_\alpha}$ is the algebra of analytic functions…