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．     

拟遗传Nakayama代数

本文分别给出了拟遗传Nakayama代数和拟遗传左serial代数的整体维数等于2或3的充分条件。     

有足够幂等元的群分次环上的Morita对偶

首先定义了具有足够幂等元的群分次环的Ｓｍ ａｓｈ 积并讨论其性质,其次,借助Ｓｍ ａｓｈ 积给出了这类分环上的分次Ｍｏｒｉｔａ对偶的刻划．     

On Galois Coverings of the Enveloping Algebras of Self-Injective Nakayama Algebras

Abstract

There is constructed a Galois covering F of the enveloping K-algebra A ^e of a self-injective Nakayama K-algebra A such that the right A ^e -module A is of the first kind with respect to F. Then, with the help of the constructed Galois covering, the Auslander-Reiten translation period of A is computed.     

以幂零李代数R_n为幂零根基的可解李代数(英文)

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.     

Algebras Generated by Semicentral Idempotents

Let be a unital K-algebra, where K is a commutative ring with unity. An idempotent is {\it left semicentral\/} if , and is {\it SCI-generated\/} if it is generated as a K-module by left semicentral idempotents. This paper develops the basic properties of SCI-generated algebras and characterizes those that are also prime, semiprime, primitive, or subdirectly irreducible. Minimal ideals and the socle of SCI-generated algebras are investigated. Conditions are found to describe a large class of SCI-generated algebras via generalized triangular matrix representations. SCI-generated piecewise domains are characterized. Examples are given that illustrate the breadth and diversity of the class of SCI-generated algebras.     

Graded automorphism group of TKK algebra

The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)).     

Spectral Radius Algebras of Idempotents

We show that the spectral radius algebras of certain quadratic operators possess nontrivial invariant subspaces. Additionally, such algebras properly contain the operator’s commutant, so that the invariant subspaces are in some sense beyond hyperinvariant. The spectral radius algebras of idempotents are completely described and, as a consequence, it is shown that every intransitive collection of operators must be contained in a norm-closed proper spectral radius algebra.      

Invariants for Automorphisms of the Underlying Algebras Relative to Lie Algebras of Cartan Type

Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.     

Boolean Algebras with Finite Families of Computable Automorphisms

We prove that each computable Boolean algebra has a computable presentation in which for every computable family of automorphisms the set of atoms moved by at least one of its members is finite. This implies that each computable atomic Boolean algebra has a computable presentation in which its every computable family of automorphisms is finite. The priority argument is not used in the proof.     

Tilting Modules Over Quasi-Hereditary Nakayama Algebras #

The structure of Ringel duals of quasi-hereditary Nakayama algebras and of quasi-hereditary left serial algebras is described.     

Frobenius Full Matrix Algebras and Gorenstein Tiled Orders

It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be extended to the category σ[M] of modules subgenerated by a module M, provided that M is a Noetherian quasi-projective generator in σ[M]. Furthermore, under this hypothesis the prime M-ideals are the fully invariant submodules P of M such that M/P is semi-compressible.     

交换半环上三角矩阵代数的自同构

证明了如果尺是含有恒等元的交换半环，那么R上的n阶上三角矩阵代数的自同构都是内自同构．     

C~*标准代数中效应的序列同构

主要借助于C~*标准算子代数中的有限秩算子对一般的效应元进行刻画.证明了C~*标准算子代数A的效应代数E(A)上的每个序列自同构和自同构ψ都具有形式ψ(A)=UAU~*,其中A∈E(A),U为酉算子或反酉算子.     

On The Number of Simple and Projective Modules in the Quasi-Tubes of Self-Injective Algebras

We establish a bound on the number of simple and projective modules in the quasi-tubes of the Auslander–Reiten quivers of finite dimensional self-injective algebras over a field.     

Co-Point Modules Over Frobenius Koszul Algebras

Let A be a Frobenius Koszul algebra such that its Koszul dual A ^! is a quantum polynomial algebra. Co-point modules over A were defined as dual notion of point modules over A ^! with respect to the Koszul duality. In this article, we will see that various important functors between module categories over A used in representation theory of finite dimensional algebras send co-point modules to co-point modules. As a consequence, we will show that if (E, σ) is a geometric pair associated to A ^!, then the map σ:E → E is an automorphism of the point scheme E of A ^!, so that there is a bijection between isomorphism classes of left point modules over A ^! and those of right point modules over A ^!.