Hom-Hopf 代数上的交叉积

在Hom-Hopf代数上,定义了Hom-交叉积的概念．并且,得到了它的两种特殊形式：Hom-smash积和Hom-扭积．并且,给出了Hom-扭积是Hom—Hopf代数的充要条件．     

Frobenius Hom-代数的二重结构与Connes余循环

本文具体的、系统的研究了Frobenius Hom-代数的二重结构, 并引入了O-算子与Hom-dendriform代数的密切关系.此外,研究Hom-dendriform代数上的Connes余循环的二重结构.最后,给出反对称无穷小Hom-双代数与Hom-dendriform D-双代数的类比关系.     

扭Heisenberg-Virasoro代数上Hom-李代数结构

Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.扭Heisenberg-Virasoro代数是次数不超过1的微分算子代数的中心扩张,它是一类重要的无限维李代数,与一些曲线的模空间有关.文章主要研究扭Heisenberg-Virasoro代数上Hom-李代数结构,确定了扭Heisenberg-Virasoro代数上存在非平凡的Hom-李代数结构.     

Hom-Hopf代数上的L-Rsmash积

在Hom-Hopf代数上,定义了L-R smash积概念并讨论了它的相关性质,给出了L-R smash积是Hom-Hopf代数的充要条件.     

Hom-弱Hopf代数上的Hom-smash积

本文研究了在Hom-Hopf代数上引入Hom-弱Hop代数的问题.通过建立弱左H-模Hom-代数的方法,构造Hom-smash积,证明Hom-smash积是Hom-代数,且给出使之成为Hom-弱Hopf代数的充分条件,推广了由Bohm等人定义的弱Hop代数.     

Hom-弱Hopf代数上的Hom-smash余积

本文研究了在Hom-Hopf代数上引入Hom-弱Hopf代数的问题.利用建立弱左H-Hom-余模双代数的方法,获得了Hom-smash余积的代数结构,并证明了Hom-smash余积是Hom-余代数和Hom-弱Hopf代数,推广了由Molnar定义的smash余积Hopf代数.     

Hom-李-Yamaguti代数上的相对罗巴算子

本文引入Hom-李-Yamaguti代数上相对罗巴算子的概念,并利用Nijenhuis算子和图给出相对罗巴算子的等价刻画.随后,引入Hom-李-Yamaguti代数上相对罗巴算子的上同调理论.最后,利用上同调方法探讨相对罗巴算子的形变.     

正则FI代数的若干性质

讨论正则FI代数的若干性质。在研究FI代数与Boole代数间关系的同时,给出正则FI代数与BCK代数的另一种联系方式。     

分裂的正则双Hom-李Color代数

本文研究了任意分裂的正则双Hom-李color代数的结构.利用此种代数的根连通,得到了带有对称根系的分裂的正则双Hom-李color代数.L可以表示成L=U+ ∑[α]∈A/～ I[α],其中U是交换(阶化)子代数H的子空间,任意I[α]为L的理想,并且满足当[α]≠[β]时,[I[α],I[β]=0.在一定条件下,定...     

分配的Fuzzy蕴涵代数

给出了分配的Fuzzy蕴涵代数的定义并探讨了其有关性质，接着本文证明了分配的Fuzzy蕴涵代数与Boole代数、正则的HFI代数是相互等价的，从而得到Boole代数的两个等价形式，并且证明了分配的Fuzzy蕴涵代数是BL代数，最后得到了FI代数成为Boole代数的几个充要条件。     

Standardly Stratified Extension Algebras

Abstract

The paper generalizes some of our previous results on quasi-hereditary Koszul algebras to graded standardly stratified Koszul algebras. The main result states that the class of standardly stratified algebras for which the left standard modules as well as the right proper standard modules possess a linear projective resolution – the so called linearly stratified algebras – is closed under forming their Yoneda extension algebras. This is proved using the technique of Hilbert and Poincaré series of the corresponding modules.

     

On Restricted Leibniz Algebras

ABSTRACT

The role played by fields in relation to Galois Rings corresponds to semifields if the associativity is dropped, that is, if we consider Generalized Galois Rings instead of (associative) Galois rings. If S is a Galois ring and pS is the set of zero divisors in S, S* = S\ pS is known to be a finite {multiplicative} Abelian group that is cyclic if, and only if, S is a finite field, or S = ?/n? with n = 4 or n = p ^r for some odd prime p. Without associativity, S* is not a group, but a loop. The question of when this loop can be generated by a single element is addressed in this article.     

Cellularity of a New Class of Diagram Algebras

A diagram algebra in which the diagrams include n rows of n points is constructed. Moreover, we prove that the algebra is cellular and quasi-hereditary.     

Generalization of quasi-Koszul algebras

In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and K p algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of K p algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-K p algebra.     

The Yoneda Algebra of a 𝒦2 Algebra Need not be Another 𝒦2 Algebra

The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. 𝒦₂ algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a 𝒦₂ algebra would be another 𝒦₂ algebra. We show that this is not necessarily the case by constructing a monomial 𝒦₂ algebra for which the corresponding Yoneda algebra is not 𝒦₂.     

Simple sagle algebras

It is proved that ifS is a simple finite-dimensional anticommutative algebra over a field ϕ of characteristic zero satisfying the identityJ(x, y, z)t=J(t, z, xy)+J(t, y, zx)+J(t, x,yz), whereJ(x, y, z)=(xy)z+(zx)y+(yz)x, thenS is a Lie algebra. Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 607–611, April, 1999.     

Graded extended Lie-type algebras

The class of extended Lie-type algebras contains the ones of associative algebras, Lie algebras, Leibniz algebras, dual Leibniz algebras, pre-Lie algebras, and Lie-type algebras, etc. We focus on the class of extended Lie-type algebras graded by an Abelian group G and study its structure, by stating, under certain conditions, a second Wedderburn-type theorem for this class of algebras.     

On Derivations of the Ternary Malcev Algebra M 8

Derivations of the simple ternary Malcev algebra M ₈ and its algebra of multiplications are described.     

Generalizing the notion of Koszul algebra

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class.