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	1. Cyclic complexes, Hall polynomials and simple Lie algebras
	Chen Qinghua, Deng Bangming
	Mathematics 30 October 2014
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	Abstract:In this paper we study the category $C_m(scrP)$ of $m$-cycliccomplexes over $scrP$, where $scrP$ is the category of projectivemodules over a finite dimensional hereditary algebra $A$, and describe almost splitsequences in $C_m(scrP)$. This is applied to prove the existence of Hall polynomials in $C_m(scrP)$when $A$ is representation finite and $m ot=1$. We furtherintroduce the Hall algebra of $C_m(scrP)$ and its localization in the sense of Bridgeland.In the case when $A$ is representation finite, we use Hallpolynomials to define the generic Bridgeland--Hall algebra of $A$and show that it contains a subalgebra isomorphic to the integralform of the corresponding quantum enveloping algebra. This providesa construction of the simple Lie algebra associated with $A$.
	TO cite this article:Chen Qinghua, Deng Bangming. Cyclic complexes, Hall polynomials and simple Lie algebras[OL].[30 October 2014] http://en.paper.edu.cn/en_releasepaper/content/4615000


	2. On S-semiembedded subgroups of finite groups
	Abid Mahboob,Yuemei Mao,Wenbin Guo
	Mathematics 03 March 2014
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	Abstract:A subgroup $H$ of a finite group $G$ is said to be $s$-semipermutable in $G$ if it is permutable with every Sylow $p$-subgroup of $G$ with $(p, \|H\|)=1$. We say that a subgroup $H$ of a finite group $G$ is $S$-semiembedded in $G$ if there exists an $s$-permutable subgroup $T$ of $G$ such that $TH$ is $s$-permutable in $G$ and $Tcap Hleq H_{ar{s}G}$, where $H_{ar{s}G}$ is an $s$-semipermutable subgroup of $G$ contained in $H$. In this paper, we investigate the influence of $S$-semiembedded subgroups on the structure of finite groups.
	TO cite this article:Abid Mahboob,Yuemei Mao,Wenbin Guo. On S-semiembedded subgroups of finite groups[OL].[ 3 March 2014] http://en.paper.edu.cn/en_releasepaper/content/4588420

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	3. A construction of stable equivalences of Morita type
	Hu Wei
	Mathematics 27 December 2013
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	Abstract:Stable equivalences of Morita type is a basic equivalent relation between finite dimensional algebras, introduced by Brou'{e} in the study of modular representation theory of finite groups. It is closely related to the famous Abelian Defect Group Conjecture. Later, Liu and Xi give a series of methods to construct stable equivalences of Morita type between general finite dimensional algebras. In particular, they proved that: If a stable equivalence of Morita type between two basic self-injective algebras $A$ and $B$ takes the socle $soc(P)$ of an indecomposable projective-injective $A$-module $P$ to the socle $soc(P')$ of an indecomposable projective-injective $B$-module $P'$, then the quotient algebras $A/soc(A)$ and $B/soc(B)$ are stably equivalent of Morita type. In this note, generalize this result by given a more general construction of stable equivalences of Morita type. Particularly, we improve the above mentioned result by remove the condition that $A$ and $B$ are self-injective.
	TO cite this article:Hu Wei. A construction of stable equivalences of Morita type[OL].[27 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4578909


	4. Classification of irreducible Whittaker modules for a Lie algebra arising from the 2-Dimensional Torus
	Tan Shaobin, Wang Qin, Xu Chengkang
	Mathematics 20 December 2013
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	Abstract:Let $A$ be the ring of Laurent polynomials in two variables and $B$ be the set of skew derivatives of $A$.We denote by $ ilde{L}$ the semi-direct product of $A$ and $B$,let $L$ be the universal central extension of the derived Lie algebra of $ ilde{L}$.In this paper, we classify the irreducible Whittaker modules for the Lie algebra $L$.
	TO cite this article:Tan Shaobin, Wang Qin, Xu Chengkang. Classification of irreducible Whittaker modules for a Lie algebra arising from the 2-Dimensional Torus[OL].[20 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4576938


	5. Integrable representations for the extended affine Lie algebra coordinated by quantum tori in two variables
	Fei Kong, Zhiqiang Li, Shaobin Tan,Qing Wang
	Mathematics 20 December 2013
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	Abstract:In this paper one classify the irreducible integrable modules for thecore of the extended affine Lie algebra of type $A_{d-1}$coordinated by $C_q$ with finite dimensional weight spaces and thecenter acting trivially, where $C_q$ is the quantum torus in twovariables.
	TO cite this article:Fei Kong, Zhiqiang Li, Shaobin Tan, et al. Integrable representations for the extended affine Lie algebra coordinated by quantum tori in two variables[OL].[20 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4576424


	6. A nonsimple Lie conformal algebra of rank 2
	YUAN Lamei,YOU Hong
	Mathematics 10 December 2013
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	Abstract:Conformal derivations, centralextensions, free rankone conformal modules and low-dimensional cohomologies of a rank $2$ Lie conformal algebraassociated to the centerless $W(2,2)$ Lie algebra are determined.
	TO cite this article:YUAN Lamei,YOU Hong. A nonsimple Lie conformal algebra of rank 2[OL].[10 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4573392


	7. Iterated almost $u$-stable derived equivalences
	Hu Wei
	Mathematics 05 December 2013
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	Abstract:The notion of derived equivalence and that of stable equivalence is mutually independent for general algebras. However, iterated almost $ u$-stable derived equivalences always induce stable equivalences between algebras. In this note, we give a new proof that an iterated almost $ u$-stable derived equivalence always induce a stable equivalence. First, we prove that the stable category modulo $ u$-stably projective modules can be embedded into the singularity category of the same algebra; Second, we show that the embedding is an equivalence if and only if the algebra is self-injective. This generalizes a result of Rickard. Finally, it is shown that an iterated almost $ u$-stable derived equivalence gives rise to an equivalence between the stable categories modulo $ u$-stably projective modules, and consequently provide a stable equivalence.
	TO cite this article:Hu Wei. Iterated almost $u$-stable derived equivalences[OL].[ 5 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4573179


	8. An Application of Subgroup-lattice Theory
	YANG YIchuan,Wang Lu
	Mathematics 21 November 2013
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	Abstract:It is well-known that a finite group $G$ is cyclic iff $G$ has at most one subgroup of each order dividing $\|G\|$. There are several proofs of this result. For instance, a popular proof of this theorem is based upon a result of number theory about Euler's totient function. As an application of subgroup lattice theory, we give new proof in this paper.
	TO cite this article:YANG YIchuan,Wang Lu. An Application of Subgroup-lattice Theory[OL].[21 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4569882


	9. Note on Classification of 2 dimensional associative lattice-ordered real algebras\
	YANG Yichuan%,ZHANG Xiaohong
	Mathematics 15 November 2013
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	Abstract:Birkhoff-Pierce give a classification of 2 dimensional associative lattice-ordered real algebras. However, there are lots of typos and other problems in the paper. In this note, wecorrect three classes of Birkhoff-Pierce's classification of 2 dimensional associative lattice-ordered real algebras.
	TO cite this article:YANG Yichuan%,ZHANG Xiaohong. Note on Classification of 2 dimensional associative lattice-ordered real algebras\[OL].[15 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4569589


	10. A note on $p$-nilpotency of finite groups
	HUO Li-Jun,MAHBOOB Abid,GUO Wen-Bin
	Mathematics 23 October 2013
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	Abstract:In this paper, the structure of a finite group $G$ under the assumption thatthe maximal subgroups of a Sylow subgroup is eithersemi cover-avoiding or $S$-quasinormally embedded subgroups in $G$ are studied.Some new characterizations on the $p$-nilpotency of finite groups are obtained, and some known results are generalized.
	TO cite this article:HUO Li-Jun,MAHBOOB Abid,GUO Wen-Bin. A note on $p$-nilpotency of finite groups[OL].[23 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565445

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