Hopf代数余作用

对于Ｈｏｐｆ代数Ｈ上的余模代数Ａ,当Ｈ是有限维或幺模（ｕｎｉｍｏｄｕｌａｒ）时,存在由交叉积Ａ＃Ｈ^＊ｒａｔ和余不变子代数Ａ^ｃｏＨ构成的Ｍｏｒｉｔａ Ｃｏｎｔｅｘｔ．本文论证了对于任意的Ｈｏｐｆ代数Ｈ,结果仍是成立的     

关于余模代数的Hopf—Jacobson根的一些结果

设Ｈ是Ｈｏｐｆ代数，Ａ是右Ｈ－余模代数，若（，）满射，则Ｊ（Ａ＾ｃｏＨ）＝Ｌ＾Ｈ（Ａ）∩＾ｃｏＨ，而且，若Ｊ（Ａ）是余模理想，则Ｊ（Ａ＾ｃｏＨ）＝Ｊ＾Ｈ（Ａ）∩Ａ＾ｃｏＨ。     

除环的Hopf Galois扩张与Hopf模

设Ｈｏｐｆ代数Ｈ余作用于代数Ａ．本文讨论代数Ａ，余不变子代数ＡｃｏＨ及Ｓｍａｓｈ积Ａ＃Ｈ的相互关系．同时将研究Ｈｏｐｆ模，全积分及除环的ＨｏｐｆＧａｌｏｉｓ扩张．     

模任意子Hopf代数的商余代数的诱导作用

设 Ｈ是域 ｋ上的有限维 Ｈｏｐｆ代数，Ｋ为 Ｈ的任意子 Ｈｏｐｆ代数，Ａ是右 Ｈ－余模代数．设 ＝（Ｈ／Ｋ+ Ｈ）*和，且有 ｃ∈Ａ，ｔ ·ｃ＝１．本 文刻划了 Ａ作为 Ａ＃ *-模的投射性且证明了：如果Ａ／ＡＨ*是 Ｈ-Ｆｒｏｂｅｎｉｕｓ扩张， 则 Ａ ／ＡＨ*是 Ｋ－Ｆｒｏｂｅｎｉｕｓ扩张；如果 Ａ／ＡＨ*是 Ｈ－Ｇａｌｏｉｓ扩张，则 Ａ *／ＡＨ*是 Ｋ－Ｇａｌｏｉｓ扩张．     

Hopf Galois扩张与Hopf模结构定理

设Ｈ是域ｋ上任意的Ｈｏｐｆ代数。本文首先讨论了右Ｈ＿扩张Ａ／Ａ￣（ｃｏＨ）与Ｈｏｐｆ模范畴，给出了Ａ／Ａ￣（ｃｏＨ）为右Ｈ－Ｇａｌｏｉｓ扩张的充分必要条件和Ｈｏｐｆ模范畴满足结构定理的若干等价条件．然后我们讨论了不可约作用与除环的Ｇａｌｏｉｓ扩张．     

不可分素C^k—代数与本原C^＊—代数的讨论

本文证明：若Ａ是不可分的素Ｃ＾＊－代数，且包含非０的Ｌｉｍｉｎａｌ遗传Ｃ＾＊－子代数，则Ａ是本原Ｃ＾＊－代数，本文还给出了Ｉ型Ｃ＾＊－代数为本原Ｃ＾＊－代数的充要条件。     

Hopf余模代数Smash积的理想

Ｈｏｐｆ余模代数Ｓｍａｓｈ积的理想陈惠香（扬州大学师范学院，扬州２２５００２）本文恒设Ｈ是域ｋ上Ｈｏｐｆ代数，Ｓ为Ｈ的ａｎｔｉｐｏｄｅ，Ｈ“为Ｈ的对偶代数。如果Ｓ是双射，则用工表示Ｓ的逆映射．有关记号参阅文ｏｆ］．设Ａ是右Ｈ一余模代数．则自然嵌人Ａ①...     

环的Galois,分离和Frobenius扩张

设∧是其中心Ｃ＿∧上的有限维单代数，Ｆ是满足Ｃ＿∧的∧的子环，Ｇ是保持Γ的元素不变的∧的自同构的有限群．本文证明：若∧／Γ是Ｇ－Ｇａｌｏｉｓ扩张，则在∧中的中心化子△是Ｃ＿Γ一分离代数且∧／Γ是Ｆｒｏｂｅｎｉｕｓ扩张，这里Ｃ＿Γ是Γ的中心．     

半群上的非交换调和分析

设Ａ（Ｍ）是 Ｃ＊－代数（ｖｏｎ Ｎｅｕｍａｎｎ代数）．本文证明了，若φ是定义在Ｒ＋上取值于Ａ（Ｍ）的范数连续的有界正定函数，则φ可表示为Ｒ＋上取值于Ａ＇＇（Ｍ）的有界半变差向量测度的Ｌａｐｌａｃｅ变换．同时也证明了取值于Ａ（Ｍ）的Ｈａｍｂｕｒｇｅｒ型的矩量问题．     

Nest代数的Jacobson根的μ-核值保持映射

设算子代数Ａ　Ｂ（Ｈ），μ（Ａ）表示Ａ中的部分等距算子全体，若ｐ是Ａ到Ｂ（Ｈ）的线性映射，且对任意的ＵＥｕ（Ａ），有叫Ｕ）（ｋｅｃＵ）Ｇｒ“ｈＣｒ，则称　是Ａ上的μ－核值保持映射。本文将证明：Ｎｅｓｔ代数的Ｊａｃｏｂｓｏｎ根上的范数拓扑连续的μ－核值保持映射是广义内导子。     

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.     

A construction of quasi-hereditary endomorphism algebras简

In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary 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.     

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.     

QF代数的Hopf代数作用

Ｈ是 Ｈｏｐｆ代数，Ａ是左 Ｈ－模代数，本文给出了当 Ａ是 ＱＦ代数时，ＡＨ也是 ＱＦ代数的一个条件．     

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.     

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.