Zhihua Chang
In this paper, we study the structure and representability of the automorphism group functor of the N=4 Lie conformal superalgebra over an algebraically closed field k of characteristic zero.
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The Kac Jordan superalgebra: automorphisms and maximal subalgebras
给出了Kac Jordan超代数的自同构自同构群，并利用自同构群对极大子代数进行了分类.
Filtration, automorphisms and classification of the infinite dimensional odd Contact superalgebras superalgebras
通过研究ad-幂零元幂零元，并确定由ad-幂零元幂零元生成的子代数等不变量，证明了特征$p>2$域上无限维奇Contact李超代数的主滤子在自同构群下是不变的.然后，证明了两个自同构重合当且仅当它们在关于主分次的-1分量上重合。最后，所有的奇Contact超代数被分类到同构。
Automorphism groups of the finite dimensional special odd Hamiltonian superalgebras in prime characteristic
研究了素特征域上三个有限维特殊奇Hamilton超代数系列$\mathfrak{g}$的自同构群.我们的目的是刻画$\mathfrak{g}$的自同构群与相应的基础超代数的自同构群之间的联系。准确地说，我们将前者嵌入后者。此外，我们还确定了$\mathfrak{g.}$的自同构群和齐次自同构群的正规列的象
Automorphisms and twisted loop algebras of finite dimensional simple Lie superalgebras
本文描述了有限维单李超代数的自同构的代数群的结构。利用这一点和平展上同调的考虑，我们列出了相应的扭圈超代数的所有不同的同构类。
Automorphisms of toroidal Lie superalgebras
给出了特征为0的代数闭域k上的简单有限维李超代数g的自同构代数群Aut（g）的详细描述。当R是具有平凡Picard群的Noether整环时，我们给出了k-李超代数$g \otimes_k R$的自同构群的描述.
Given an algebraically closed field $\Bbbk$ of characteristic zero, a Lie superalgebra $\mathfrak{g}$ over $\Bbbk$ and an associative, commutative $\Bbbk$-algebra $A$ with unit, a Lie superalgebra of the form $\mathfrak{g} \otimes_\Bbbk A$ is known as a map superalgebra. Map superalgebras generalize important classes of Lie superalgebras, such as, loop superalgebras (where $A=\Bbbk[t, t^{-1}]$), and current superalgebras (where $A=\Bbbk[t]$). In this paper, we define Weyl functors, global and local Weyl modules for all map superalgebras where $\mathfrak{g}$ is either $\mathfrak{sl} (n,n)$ with…
Let $F$ be a field of characteristic zero and let $E$ be the Grassmann algebra of an infinite dimensional $F$-vector space $L$. In this paper we study the superalgebra structures (that is the $\mathbb{Z}_{2}$-gradings) that the algebra $E$ admits. By using the duality between superalgebras and automorphisms of order $2$ we prove that in many cases the $\mathbb{Z}_{2}$-graded polynomial identities for such structures coincide with the $\mathbb{Z}_{2}$-graded polynomial identities of the "typical" cases $E_{\infty}$, $E_{k^\ast}$ and $E_{k}$ where the vector space $L$ is homogeneous. Recall that…
Spin polynomial functors and representations of Schur superalgebras
我们引进类齐次严格多项式函子，$\Pol^\I_{d,\k}$和$\Pol^\II_{d,\k}$，定义在域$\k$的特征不等于2的向量超空间。这些范畴分别与超群$GL(m|n)$和Q（n）的多项式表示有关。特别地，我们证明了在$m,n \ge d$的条件下，Schur超代数$\Sc(m|n,d)$，$\Qc(n,d)$上的有限维超模范畴$\Pol^\I_{d,\k}$，$\Pol^\II_{d,\k}$与它们之间的等价性.我们还从范畴$\Pol^\II_{d,\k}$的角度讨论了Sergeev对偶的某些方面。
On real forms of complex Lie superalgebras and complex algebraic supergroups
本文涉及两个版本的概念实形式的李超代数。一种是标准方法，其中复李超代数的实形式是实李超代数，使得它的复化是原复李超代数。第二个问题涉及到考虑具有超共轭的交换复超代数$A$上李超代数的$A$ -点。不难看出，第一个实形式可以作为一个反线性对合自同构的不动点集得到，第二个实形式与一个自同构$ϕ$有关，使得$ϕ^{2}$在偶数部分是恒等式，在奇数部分是负恒等式。实形式的广义概念随后也被引入复代数超群。
In this paper we describe all subalgebras and automorphisms of simple noncommutative Jordan superalgebras $K_3(α,β,γ)$ and $D_t(α,β,γ)$ and compute the derivations of the nontrivial simple finite-dimensional noncommutative Jordan superalgebras.
This paper is devoted to investigating the structure theory of a class of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we completely determine the derivation algebras, the automorphism groups and the second cohomology groups of these Lie superalgebras.
Automorphisms and twisted forms of the N = 1, 2, 3 Lie conformal superalgebras
我们利用微分非交换上同调对Schwimmer和Seiberg的N = 1，2，3超共形李代数进行了分类，并描述了这种新方法背后的一般原理.相应的李共形超代数的自同构群（函子）的结构是证明的关键要素。
Semisimplifying Lie algebras of $J$-ternary algebras in characteristic $3$
本文在特征3下通过半简化函子构造了$J$-ternary代数的李超代数，并扩展了Elduque超代数的构造方法。
On twisted large N=4 conformal superalgebras
我们明确地计算了N = 4大共形超代数的自同构群，并基于N = 4大共形超代数对扭圈共形超代数进行了分类。通过考虑相应的超共形李代数，我们验证了物理学文献中描述的只有两个（直到同构）这样的代数的存在。
Interplay between $\mathbb{Z}_2$-gradings and automorphisms in the Grassmann algebra: a survey
本文综述了特征不为二的域上格拉斯曼代数的二阶自同构及其诱导的超代数结构，给出非齐次自同构实例，并提出超代数结构分类猜想。
The group-scheme of automorphisms of the ten-dimensional exceptional Kac's Jordan superalgebra is shown to be isomorphic to the semidirect product of the direct product of two copies of SL2 by the constant group scheme C2. This is used to revisit, extend, and simplify, known results on the classification of the twisted forms of this superalgebra and of its gradings.
Lie conformal superalgebras of rank (2 + 1)
本文完全分类了秩为 (2 + 1) 的李共形超代数及其自同构群，并进一步分类了其上的有限不可约共形模，同时显式描述了模作用。
Lie superalgebras of differential operators
我们明确描述李超代数同构的一阶超微分算子的李超代数的超流形，特别是任何这样的同构诱导的超流形的一个超同构。我们还证明了这样的李超代数的自同构自同构群是由超流形自同构诱导的子群与由偶超发散确定的自同构构成的另一个子群的半直积。证明了这些超发散存在于任意的超流形上，并给出了它们的局部形式
Differential Conformal Superalgebras and their Forms
我们介绍了微分共形超代数的形式主义，我们表明导致“正确的”自同构群函子和伴随的下降理论的共形设置。作为应用，我们利用Galois上同调对N=2和N=4共形超代数的形式进行了分类.
Group gradings on exceptional simple Lie superalgebras
本文在特征0代数闭域上同构分类了例外单李超代数$G(3)$、$F(4)$、$D(2,1;α)$及$A(1,1)$上的任意群分次，核心方法是将Elduque等的新方法应用于已知的精细分次等价分类。
The parity of Lusztig's restriction functor and Green's formula for a quiver with automorphism
本文将Fang-Lan-Xiao关于Lusztig诱导与限制函子的公式推广至带自同构箭图的混合半单反常层，并通过迹映射导出了有限域上任意有限维遗传代数的Green公式。
Automorphism group functors of algebraic superschemes
本文将Matsumura-Oort关于本征概形自同构群函子为局部代数群概形的定理推广到超概形范畴，并在一阶上同调消失条件下证明其为光滑群超概形。
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real forms as fixed points, as in the ordinary setting. We also introduce a more general notion of compact real form for Lie superalgebras and supergroups, and we prove some existence results for Lie superalgebras that are simple contragredient and their associated connected simply connected supergroups.
Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie superalgebras, and generalize a result from \cite{CM} about twisting Verma modules.
The Image of Functor Morphing
本文研究了函子变形的像，通过抛物子群作用提出判别准则，并在有限域的博雷尔群上验证。
Two classes of Lie conformal superalgebras related to the Heisenberg--Virasoro Lie conformal algebra
本文构造了两类与Heisenberg-Virasoro李共形超代数相关的李共形超代数$\mathcal{HVS}(α)$和$\mathcal{HVS}(β,γ,τ)$，并完全确定了它们的共形导子、共形双导子、自同构群及秩$(1+1)$的共形模。
On some derivations of Lie conformal superalgebras
本文研究 Lie 共形超代数上的共形导子、三重导子及广义情形，完成有限单情形分类，并引入 $(A,B,C,D)$-导子与三重同态。
An inner automorphism is only an inner automorphism, but an inner endomorphism can be something strange
群G的内自同构可以在不涉及群元素的群范畴内刻画：它们正是G的那些自同构，它们可以以函子的方式推广到所有具有同态G --> H的群H。与G自身的内自同构群不同，这种扩张的自同构系群总是同构于G。一个类似的特征也适用于域K上的结合代数R的内自同构;这里自同构的函子系群同构于R的单位群模K的单位。如果在这些考虑中用“自同态”代替“自同构”，那么在群的情况下，唯一的额外例子是平凡自同态;但是在K-代数的情况下，一个环理论家不熟悉但泛函分析家熟悉的结构也出现了。系统的自同态具有相同的函性质检查在其他一些类别;其他使用的短语“内自同态”在文献中，一些重叠的介绍，注意到;的概念内{ \em导子}的结合或李代数是看从同一个角度来看，和对偶概念的“co-inner”自同态进行了简要的检查。提出了几个问题。
We generalise notions of Gorenstein homological algebra for rings to the context of arbitrary abelian categories. The results are strongest for module categories of rngs with enough idempotents. We also reformulate the notion of Frobenius extensions of noetherian rings into a setting which allows for direct generalisation to arbitrary abelian categories. The abstract theory is then applied to the BGG category O for Lie superalgebras, which can now be seen as a "Frobenius extension" of the corresponding category for the underlying Lie algebra and is therefore "Gorenstein". In particular we obta…
Let $ 0\rightarrow \mathfrak{a} \rightarrow \mathfrak{e} \rightarrow \mathfrak{g} \rightarrow 0$ be an abelian extension of the Lie superalgebra $\mathfrak{g}$. In this article we consider the problems of extending endomorphisms of $\mathfrak{a}$ and lifting endomorphisms of $\mathfrak{g}$ to certain endomorphisms of $\mathfrak{e}$. We connect these problems to the cohomology of $\mathfrak{g}$ with coefficients in $\mathfrak{a}$ through construction of two exact sequences, which is our main result, involving various endomorphism groups and the second cohomology. The first exact sequence is obt…
Classification of irreducible real modules of real Lie superalgebras
本文通过研究奇性与共轭泛函的轨道来分类实丽超代数的不可约有限维模，揭示了实简单李代数模分类的新视角及与Kostant强正交根 cascade 的联系。
The Automorphism Group of a Metropolis-Rota Implication Algebra
讨论了一般MR-代数的自同构自同构群。我们在蕴涵代数和三次代数之间发展了几个函子。这些使我们能够推广内自同构的概念。然后我们证明了这个群总是同构于滤子代数的内自同构群。
Applications of BGP-reflection functors: isomorphisms of cluster algebras
给定一个可对称化的广义Cartan矩阵$A$，对于任何指标$k$，可以定义一个与$n$独立不定式的有理函数的域$\mathbf{Q}(u_1, >..., u_n)$的$A,$相关的自同构$u_1,..., u_n.$它是与矩阵$A$相关的两个簇代数之间的同构（精确含义见第4节）。当$A$是有限型时，这些同构表现得很好，如果我们用相应的簇代数的簇变量来标识簇范畴中的不可分解对象，它们与[Z1，Z2]中定义的簇范畴的BGP-反射函子相容，并且它们也与[FZ 2，FZ 3]中定义的“截断简单反射”相容.利用Dlab-Ringel [DR]对遗传代数的预投射或预内射模的构造和Coxeter自同构（即，这些同构的乘积），我们构造了无限型簇代数的无限多个簇变量和有限型的所有簇变量。
Let k be a field of characteristic 0. Let G be a reductive group over the ring of Laurent polynomials R=k[x_1^{\pm 1},...,x_n^{\pm 1}] containing a maximal R-torus T (equivalently, loop reductive). Assume also that every semisimple normal subgroup of G contains a two-dimensional split torus G_m^2. We show that the natural map of non-stable K_1-functors K_1^G(R)-> K_1^G(k((x_1))...((x_n))) is injective. This complements the surjectivity result for the same map obtained by V. Chernousov, P. Gille and A. Pianzola in arXiv:1109.5236. As a corollary, we provide a way to evaluate the difference betw…
$(d,σ)$-twisted Affine-Virasoro superalgebras
本文引入了带有偶导子和有限阶自同构的 $(d,σ)$-扭曲 Affine-Virasoro 超代数及其泛中心扩张，并利用权函子和 $A$-覆盖方法完成了对其单尖点模与单拟有限模的分类。
Milnor-Moore Categories and Monadic Decomposition
本文在Eilenberg-Moore范畴的基础上，通过构造函子的一元分解，得到了Hom-李代数、李色代数、李超代数和其它类型的广义李代数.为此目的，我们引入Milnor-Moore范畴作为一个幺半范畴的概念，并证明了Milnor-Moore型定理。我们还展示了如何解除的性质是一个Milnor-Moore范畴时，一个合适的monoidal函子，我们应用这种技术提供的例子。
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a Krull-Schmidt category on which a finite group acts as automorphisms. This then provides the orbit category introduced by Cibils and Marcos, and studied intensively by Keller in the context of cluster algebras, and by Asashiba in the context of Galois covering functors. We formulate and prove Clifford's theorem for Krull-Schmidt orbit categories with respect to a finite…
Solenoids in automorphism groups of evolution algebras
该研究刻画了演化代数中相对于自然基可对角化的自同构群，将其表示为关联图对应函子的逆极限，部分情形下可实现为二元螺线管，并完整描述了满足2LI条件的代数的自同构群。
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