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	1. On the Green rings of finite dimensional Hopf algebras
	Zhihua Wang,, Yin-huo Zhang
	Mathematics 31 May 2016
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	Abstract: When $H$ is an arbitrary finite dimensional Hopf algebra over an algebraically closed field, we character whether or not the trivial module appears as a direct summand of the tensor product for any two indecomposable modules. We use these characterizations to obtain some one-sided ideals of the Green ring of Hopf algebra $H$. This allows us to study the nilpotent radical and central primitive idempotents of the Green ring. We study the Green ring of $H$ by virtue of bilinear forms. If $H$ is of finite representation type, the Green ring is a Frobenius algebra over $mathbb{Z}$ with the dual basis associated to almost split sequences.
	TO cite this article:Zhihua Wang,, Yin-huo Zhang. On the Green rings of finite dimensional Hopf algebras[OL].[31 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693663


	2. New classes of complete permutation polynomials
	MA Jingxue, ZHANG Tao, DING Baokun, FENG Tao, GE Gennian
	Mathematics 24 May 2016
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	Abstract:In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented. In addition, we also give two classes of trinomial permutation polynomials. The first class of monomial complete permutation polynomials is a conjecture proposed by Wu et al. (arXiv:1312.4716).
	TO cite this article:MA Jingxue, ZHANG Tao, DING Baokun, et al. New classes of complete permutation polynomials[OL].[24 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693433

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	3. On the center of the quantized enveloping algebra of a semisimple Lie algebra
	Li-bin Li,Li-meng Xia, Yin-huo Zhang
	Mathematics 24 May 2016
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	Abstract: Let $sg$ be a complex simple finite dimensional Lie algebra and $U=U_q(sg)$ the quantized enveloping algebra in Jantzen's sense with $q$ being generic. In this paper, we prove that the center $Z(U_q(sg))$ of the quantum group $U_{q}(sg)$ is isomorphic to a monoid algebra, and $Z(U_q(sg))$ is a polynomial algebra if and only if $sg$ is of type $A_1, B_n, C_n, D_{2k+2}, E_7, E_8, F_4$ and $G_2.$ It turns out that when $sg$ is of type $D_{n}$ with $n$ odd then $Z(U_q(sg))$ is isomorphic to a quotient algebra of polynomial algebra with $n+1$ variables and one relation, and while when $sg$ is of type $E_6$ then $Z(U_q(sg))$ is isomorphic to a quotient algebra of polynomial algebra with fourteen variables and eight relations.
	TO cite this article:Li-bin Li,Li-meng Xia, Yin-huo Zhang. On the center of the quantized enveloping algebra of a semisimple Lie algebra[OL].[24 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4693188


	4. Weak Hopf Algebras Corresponding to Non-standard Quantum Groups
	CHENG Cheng,YANG Shi-Lin
	Mathematics 11 December 2015
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	Abstract: We construct a weak Hopf algebra $wx$ corresponding to non-standard quantum group $X_q(A_1)$.The PBW basis of $wx$ is described and all the highest weight modules of $wx$ are classified.Finally we give the Clebsch-Gordan decomposition of the tensor product of two highest weight modules of $wx$.
	TO cite this article:CHENG Cheng,YANG Shi-Lin. Weak Hopf Algebras Corresponding to Non-standard Quantum Groups[OL].[11 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4670719


	5. Representations of Non-standard Quantum Groups
	GAO Feng-xia,YANG Shi-lin
	Mathematics 11 December 2015
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	Abstract:It is noted that a class of non-standard quantum group $X_q(A_n)$ was introduced by some mathematicians in 1990$^prime$s. In paper we give a classification of the finite-dimensional irreducible representations of $X_q(A_2)$ and describe explicitly the basis and structure of each isomorphic class.
	TO cite this article:GAO Feng-xia,YANG Shi-lin. Representations of Non-standard Quantum Groups[OL].[11 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4670722


	6. On quasi-translations of polynomial algebras
	LIU Da-Yan,YANG Liu
	Mathematics 20 November 2015
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	Abstract:In the paper, we introduce the so-called quasi-translation, an important type of automorphisms of polynomial algebras, including the background, quasi-translation and nice derivations, the relations between quasi-translations and nilpotent Hessian matrices and the Jacobian conjecture.
	TO cite this article:LIU Da-Yan,YANG Liu. On quasi-translations of polynomial algebras[OL].[20 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4663674


	7. Retracts of polynomial algebras obtained from quasi-translations
	LIU Da-Yan
	Mathematics 20 November 2015
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	Abstract:Retracts of polynomial algebras are closely related to the study of automorphisms of polynomial algebras. In the paper, we construct some retracts of polynomial algebras by use of some special quasi-translations, and describe the structure of these retracts.
	TO cite this article:LIU Da-Yan. Retracts of polynomial algebras obtained from quasi-translations[OL].[20 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4663368


	8. Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lieconformal superalgebras
	YUAN La-Mei, CHEN Sheng, He Cai-Xia
	Mathematics 09 November 2015
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	Abstract:The purpose of this paper is to introduce and study super Hom-Gel'fand-Dorfman bialgebras and Hom-Lie conformal superalgebras. In this paper, different ways for constructing super Hom-Gel'fand-Dorfman bialgebras are provided and a class of infinite-dimensional Hom-Lie superalgebras from affinization of super Hom-Gel'fand-Dorfman bialgebras are obtained. Also, a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras is given and equivalence of quadratic Hom-Lie conformal superalgebras and super Hom-Gel'fand-Dorfman bialgebras is established. Finally, one-dimensional central extensions of quadratic Hom-Lie conformal superalgebras are studied.
	TO cite this article:YUAN La-Mei, CHEN Sheng, He Cai-Xia. Super Hom-Gel'fand-Dorfman bialgebras and Hom-Lieconformal superalgebras[OL].[ 9 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660822


	9. Investigations of $S$-posets by 1-pureproperties
	Chen Xia, Zhang Xia
	Mathematics 20 April 2015
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	Abstract:In this work, we study properties of 1-pure $S$-posetsand absolutely 1-pure $S$-posets over a pomonoid, respectively. As aresult, a characterization of an $S$-poset to be 1-pure is given andhomological classifications of a pomonoid $S$ by absolutely 1-pureproperties of $S$-posets are obtained.
	TO cite this article:Chen Xia, Zhang Xia. Investigations of $S$-posets by 1-pureproperties[OL].[20 April 2015] http://en.paper.edu.cn/en_releasepaper/content/4639342


	10. Notes on Partially Ordered Monoids
	LIU Pengyuan,YANG Yichuan,MUHAMMAD Zafrullah
	Mathematics 26 November 2014
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	Abstract:In this paper, we give the definitions of positive elements, positive cones and pri-\mal elements of partially ordered monoids. Then we consider the Riesz interpolation property of partially ordered monoids, and thus we introduce the definition of the weak Riesz interpola-\tion property of partially ordered monoids. At the same time, we consider the (pR) condition in the partially ordered groups just like in partially ordered groups, and generalize the (pR) c-\ondition to (WpR) condition. On the basis of these, we consider the Conrad's F-condition for lattice-ordered monoids, Riesz monoids, and pre-Riesz monoids.
	TO cite this article:LIU Pengyuan,YANG Yichuan,MUHAMMAD Zafrullah. Notes on Partially Ordered Monoids[OL].[26 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4620489

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