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Let (K, M, H) be an upper triangular bimodule problem. Brüstle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K, M, H) is quasi-hereditary, and there is an equivalence between the category of △-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of △-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M, H) is an upper triangular bipartite bimodule problem, then A is of △-tame representation type if and only if F(△) is homogeneous. 相似文献
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WEN Dao-wei 《高校应用数学学报(英文版)》2014,29(1):119-126
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. 相似文献
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DENG Bangming 《中国科学A辑(英文版)》2000,43(11)
This paper gives a complete classification of F (Δ)-finite twisted double incidence algebras of posets in the case where the Hasse quivers of posets are of type An. 相似文献
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张跃辉 《中国科学A辑(英文版)》2002,45(6):741-748
Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra
T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the
maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of
A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if
and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the
exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there
exists an idempotent e of A, and an invertible element u of A, such that eBe = u-1eCeu. 相似文献
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For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism. 相似文献
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Vladimir Mazorchuk 《Compositio Mathematica》1999,115(1):21-35
We constuct and investigate a structure of Verma-like modules over generalized Witt algebras. We also prove Futorny-like theorem for irreducible weight modlues whose dimensions of the weight spaces are uniformly bounded. 相似文献
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Gena Puninski 《Proceedings of the American Mathematical Society》2004,132(7):1891-1898
We prove that over every non-domestic string algebra over a countable field there exists a superdecomposable pure-injective module.
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WANG Minxiong~ LIN Yanan~.Department of Mathematics Huaqiao University Quanzhou China.Department of Mathematics Xiamen University Xiamen China 《中国科学A辑(英文版)》2005,48(1):97-106
Let T be a tilting A-module over a path algebra of Dynkin type.We prove thatif the indecomposable direct summands of T are in the different (?)-orbits of the AR-quiverof A,then T is a complete slice module. 相似文献
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In this paper, a class of generalized Verma modules M(V) over some Block type Lie algebra ℬ(G) are constructed, which are induced from nontrivial simple modules V over a subalgebra of ℬ(G). The irreducibility of M(V) is determined.
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We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard.
For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism)
a slice module is a tilting module.
The first named author was supported by the Polish Scientific Grant KBN No 1 P03A 018 27 相似文献
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Limeng XIA 《Frontiers of Mathematics in China》2020,15(3):593
For all generic , when g is not of type A1; we prove that the quantum toroidal algebra Uq(gtor) has no nontrivial finite dimensional simple module. 相似文献
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In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
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Grzegorz Bobinski 《Transactions of the American Mathematical Society》2008,360(2):717-742
We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules normality is equivalent to irreducibility.
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Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i.e., types B and D. 相似文献
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Conjugation-uniqueness of exact Borel subalgebras 总被引:3,自引:0,他引:3
Yuehui Zhang 《中国科学A辑(英文版)》1999,42(12):1246-1250
It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the
inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
Project supported by the National Natural Science Foundation of China (Grant No. 19771070). and partly supported by the NSF
of Hainan Province (Grant No. 19702) and by the Natural Science Foundation of Education Department of Hainan province. 相似文献
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代数表示论的某些新进展 总被引:1,自引:0,他引:1
代数表示理论是代数学的一个新的重要分支,在近二十五年的时间里,这一理论有很大的发展,关于代数表示的基础理论的介绍可参见文献(101),本文主要从Hall代数和拟遗传代数两个方面介绍代数表示论的一些最新进展,第一章给出了Hall代数的基本理论及其方法,并且着重指出了利用这一理论和方法通过代数表示论去实现Kac-Moody李代数及相应的量子包络代数,第二章介绍了拟遗传代数及其表示理论,以及这一理论与复 相似文献
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LIU Gongxiang & YE Yu Institute of Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2006,49(3):320-329
In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras. 相似文献