Automorphism groups and derivation algebras of finitely generated vertex operator algebras

Derivations, automorphisms and second cohomology of generalized loop Schrödinger-Virasoro algebras

The derivation algebras, automorphism groups and second cohomology groups of the generalized loop Schrödinger-Virasoro algebras are completely determined in this paper.

有限生成顶点代数的自同构群的可表示性

Representability of the automorphism group of finitely generated vertex algebras

研究自由代数的自同构群，证明有限生成顶点代数在其noetherian环上的自同构群为仿射群方案。

Twisted derivations of Hopf algebras

In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of bialgebras. Twisted derivations naturally form a Lie algebra (the tangent algebra of the group of twisted automorphisms). Moreover this Lie algebra fits into a crossed module (tangent to the crossed module of twisted automorphisms). Here we calculate this crossed module for universal enveloping algebras and for the Sweedler's Hopf algebra.

Structures of not-finitely graded Lie algebras related to generalized Virasoro algebras

In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Virasoro algebras. In particular,the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.

量子环面与量子空间的斜导子

Skew derivations of quantum tori and quantum spaces

本文研究量子环面与量子仿射空间的σ-导子结构，给出其分解形式，推广了已有结论，并将结果应用于迭代Ore扩张，提出构造量子环面的算法，还探讨了斜导子与正规化序列的联系。

Derivations of the two-parameter quantized enveloping algebra $\U$

Let $r,s$ be two parameters chosen from $\C^{\ast}$ such that $r^{m}s^{n}=1$ implies $m=n=0$. We compute the derivations of the two-parameter quantized enveloping algebra $\U$ and calculate its first degree Hochschild cohomology group. We further determine the group of algebra automorphisms for the two-parameter Hopf algebra $\V$. As a result, we determine the group of Hopf algebra automorphisms for $\V$.