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1.
We show that many Kadison–Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.  相似文献   

2.
<正>On Strong Kadison-Singer Algebras Ai Ju DONG Dong WANG Abstract We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras.Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.  相似文献   

3.
本文研究了强极大TAF代数的交不可约D-模的有关性质.利用矩阵单元链的方法,证明了全上三角矩阵代数中任一D-模等于包含它的所有交不可约D-模的交,建立了强极大TAF代数的交不可约D-模与矩阵单元链之间的对应关系,推广了强极大TAF代数中关于理想的若干性质.  相似文献   

4.
We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.

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5.
Jordan isomorphisms of triangular rings   总被引:1,自引:0,他引:1  
We investigate Jordan isomorphisms of triangular rings and give a sufficient condition under which they are necessarily isomorphisms or anti-isomorphisms. As corollaries we obtain generalizations of two recent results: the one concerning Jordan isomorphisms of triangular matrix algebras by Beidar, Bresar and Chebotar, and the one concerning Jordan isomorphisms of nest algebras by Lu.

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6.
Generalized Lie derivations on triangular algebras   总被引:1,自引:0,他引:1  
Let A be a unital algebra and let M be a unitary A-bimodule. We consider generalized Lie derivations mapping from A to M. Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A.  相似文献   

7.
We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz–Happel’s theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen–Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.  相似文献   

8.
9.
本文研究了三角代数的自同构.利用三角代数的基本概念及自同构定义,得到三角代数的自同构形式,并刻画了其内自同构的具体形式.  相似文献   

10.
Characteristic tilting modules and Ringel duals   总被引:6,自引:0,他引:6  
The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbitrary hereditary algebra has triangular decomposition and bipartite quiver.  相似文献   

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