无限型代数的表示嵌入

关于极小表示无限代数

On minimal representation-infinite algebras

本文在代数闭域上对所有双边理想格非分配的极小表示无限代数进行了分类，并得出每个维度上此类代数的同构类仅有有限多个的结论。

Conformal embeddings and simple current extensions

In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.

Homological embeddings for preprojective algebras

For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only Ext$^1$ is preserved. In case $A$ is a preprojective algebra of Dynkin type, we give an explicit classification of all weakly homological and homological embeddings. Furthermore, we show that for self-injective algebras a classification of homological embeddings becomes accessible once these algebras fulfil the Tachikawa conjecture.

Malcev代数上嵌入张量的表示与上同调

Representation and cohomology of embedding tensors on Malcev algebras

本文引入Malcev代数上嵌入张量的概念，研究其表示与上同调理论，并探讨在形变与阿贝尔扩张中的应用。

混合字圈积在李代数表示中的嵌入定理

The Embedding Theorem for a Mixed Verbal Wreath Product in Lie Algebras Representations

李代数表示中的混合动词圈积是与A. L.什梅尔金证明了关于嵌入到动词圈积中的群定理的类似定理也适用于李代数的表示。

Embeddings of algebras in derived categories of surfaces

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some restrictions on those algebras whose derived categories can be embedded into the bounded derived category of a smooth projective surface. This is then applied to obtain explicit results for hereditary algebras.

The minimal representation-infinite algebras which are special biserial

Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial algebras which are minimal representation-infinite. The second part describes the corresponding module categories.

Some general results on conformal embeddings of affine vertex operator algebras

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer levels. In particular, we construct all remaining conformal embeddings associated to automorphisms of Dynkin diagrams of simple Lie algebras. The semisimplicity of the corresponding decompositions is obtained by using the concept of fusion rules for vertex operator algebras.

Indecomposable characters of infinite dimensional groups associated with operator algebras

We determine the indecomposable characters of several classes of infinite dimensional groups associated with operator algebras, including the unitary groups of arbitrary unital simple AF algebras and II$_1$ factors.

infinite dimensional李代数的Motivic zeta函数

Motivic zeta functions of infinite dimensional Lie algebras

我们将motivic zeta函数与一大类无限维李代数联系起来

The controlling $L_\infty$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples

In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an $L_\infty$-algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie-Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal deformations and central extensions using the second cohomology groups. Finally, we introduce the notion of a homotopy embedding tensor which will induce a Leibniz$_\infty$-algebra. We realize Ko…

Hom-Lie 代数上的嵌入张量

Embedding tensors on Hom-Lie algebras

本文在 Hom-Lie 代数上引入了嵌入张量，构造了刻画它的分次 Lie 代数与控制 $L_\infty$-代数，定义了相关上同调与 Hom-Lie-Leibniz 三元组，并探讨了同伦嵌入张量与 $HLeib_\infty$-代数的关系。

对偶对与infinite dimensional李代数

Dual pairs and infinite dimensional Lie algebras

我们构造并研究了有限维经典李群与无限维李代数在某些Fock表示下的各种对偶对。这里的无限维李代数可以是完备的无限秩仿射李代数、$\winf$代数或它的某些李子代数。我们在顶点代数的框架下给出了一个公式。我们还制定了几个示意图和开放的问题。

从图平面代数嵌入中获得类型$G_2$的量子子群

Type $G_2$ Quantum Subgroups from Graph Planar Algebra Embeddings

本文通过图平面代数嵌入方法，研究并展示了类型$G_2$的两个量子子群的图示表示及其生成方法。