let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.

For a finite Coxeter group, W , and its reflection representation h, we find the character and Hilbert series for a quotient ring of C[h⊕h∗] by an ideal containing the W–invariant polynomials without constant term. This confirms conjectures of Haiman.

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

We begin by recalling some well-known facts. The natural action of the symmetric group Sn on jRn can be viewed as a group generated by reflections. The reflections in Sn are the orthogonal reflections across the hyperplanes H jj = {x E jRnlxj = x j }, 1 '.5, i < j '.5, n. The Sn-action extends to Cn (= jRn ®C) and the set of points with nontrivial isotropy group is U H jj ® C. Let M denote the ...

Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.

We consider a Deligne–Mumford stack $X$ which is the quotient of an affine scheme $\operatorname {Spec}A$ by action finite group $G$ and show that Balmer spectrum tensor triangulated category perfect complexes on homeomorphic to space homogeneous prime ideals in cohomology ring $H^*(G,A)$ .