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	1. LIE ALGEBRAS IN SYMMETRIC LINEAR GR-CATEGORIES
	Hua-Lin Huang,Yuping Yang
	Mathematics 10 May 2017
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	Abstract:In this paper, we study Lie algebras in symmetric linear Gr-categories with focus on those with nontrivial associativity constraints. Such Lie algebras are natural counterparts of the well known Lie coloralgebras which live in linear Gr-categories with associativity isomorphisms being identity. We give the reduced form of the Lie algebras in symmetric linear GR-category and prove the PBW theorem which is a unified form of that for ordinary Lie algebras, Lie superalgebras and Lie coloralgebras.
	TO cite this article:Hua-Lin Huang,Yuping Yang. LIE ALGEBRAS IN SYMMETRIC LINEAR GR-CATEGORIES[OL].[10 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4732999


	2. A generalization of the doubling construction for sums of squares identities
	Chi Zhang, Hua-Lin Huang
	Mathematics 10 May 2017
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	Abstract:The doubling construction is a fast and important way to fill in the blanks of the solution table to the Hurwitz problem on sums of squares identities. By taking advantage of twisted group algebras over $Z_2^n$ and intercalate matrices, we generalize the doubling construction and obtain from any known admissible triple $[r,s,n]$ a series of new ones $[r+ ho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m,$ where $ ho$ is the Hurwitz-Radon function.
	TO cite this article:Chi Zhang, Hua-Lin Huang. A generalization of the doubling construction for sums of squares identities[OL].[10 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733002

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	3. 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


	4. 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


	5. 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


	6. 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


	7. 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


	8. 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


	9. 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


	10. Homological Dimensions Relative to Preresolving Subcategories
	Huang Zhaoyong
	Mathematics 22 October 2013
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	Abstract:We introduce relative preresolving subcategories and precoresolving subcategories of an abelian category and define homological dimensions and codimensions relative to these subcategories respectively. We study the properties of these homological dimensions and codimensions and unify some important properties possessed by some known homological dimensions. Then we apply the obtained properties to special subcategories and in particular to module categories. Finally we propose some open questions and conjectures, which are closely related to the generalized Nakayama conjecture and the strong Nakayama conjecture.
	TO cite this article:Huang Zhaoyong. Homological Dimensions Relative to Preresolving Subcategories[OL].[22 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4565406

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