Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals

具有3维交换导理想的5维可解李代数的一个子类

On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal

本文给出了MD5-代数和MD5-群类的一个子类，即，五维可解李代数和李群，使得它们在余伴随表示（K-轨道）中的轨道是零维或最大维的轨道。本文的主要结果是把所有的MD5-代数$\mathcal{G}$分类为同构，导出理想${\mathcal{G}}^{1} := [\mathcal{G}, \mathcal{G}]$是一个3维交换李代数.

关于 sl(n) 与交换理想半直积的 Jordan-Kronecker 不变量的一个注记

A note on Jordan-Kronecker invariants of semi-direct sums of sl(n) with a commutative ideal

本文补充 Vorushilov 的结果，确定 sl(n) 与交换理想半直积在 n≡±1 (mod k) 情形下的 Jordan-Kronecker 不变量。

Self-injective commutative rings have no nontrivial rigid ideals

We establish a link between trace modules and rigidity in modules over Noetherian rings. Using the theory of trace ideals we make partial progress on a question of Dao, and on the Auslander-Reiten conjecture over Artinian Gorenstein rings.

Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions

In this paper, we study divisorial ideals of a Hibi ring which is a toric ring arising from a partially ordered set. We especially characterize the special class of divisorial ideals called conic using the associated partially ordered set. Using our description of conic divisorial ideals, we also construct a module giving a non-commutative crepant resolution (= NCCR) of the Segre product of polynomial rings. Furthermore, applying the operation called mutation, we give other modules giving NCCRs of it.

The spectrum of a twisted commutative algebra

A twisted commutative algebra is (for us) a commutative $\mathbf{Q}$-algebra equipped with an action of the infinite general linear group. In such algebras the "$\mathbf{GL}$-prime" ideals assume the duties fulfilled by prime ideals in ordinary commutative algebra, and so it is crucial to understand them. Unfortunately, distinct $\mathbf{GL}$-primes can have the same radical, which obstructs one from studying them geometrically. We show that this problem can be eliminated by working with super vector spaces: doing so provides enough geometry to distinguish $\mathbf{GL}$-primes. This yields an …

Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs

The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by $\Bbbk[K_{r_1,\ldots,r_n}]$, where $1 \leq r_1 \leq \cdots \leq r_n$. More concretely, we prove that the class group of $\Bbbk[K_{r_1,\ldots,r_n}]$ is isomorphic to $\mathbb{Z}^n$ if $n =3$ with $r_1 \geq 2$ or $n \geq 4$, while it turns out that the excluded cases can be deduced into Hibi rings. The second goal is to investigate the special class of divisorial ideals of $\Bbbk[K_{r_1,\ldots,r_n}]$, called conic divisorial ideals. We describe conic divisorial ideals fo…