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1.
In this paper, topologically primitive rings and rings possessing a faithful topologically irreducible module and bounded by this module are considered for the investigation of properties of their topological Jacobson radical. We investigate the topological Jacobson radical in some classes of topological rings such as left topologically Artinian rings, topological rings possessing a basis of neighborhoods of zero consisting of ideals, compact rings, and bounded strictly linearly compact rings.  相似文献   

2.
The wreath product of finite association schemes is a natural generalization of the notion of the wreath product of finite permutation groups. We determine all irreducible representations (the Jacobson radical) of a wreath product of two finite association schemes over an algebraically closed field in terms of the irreducible representations (Jacobson radicals) of the two factors involved.  相似文献   

3.
关于二宽度CSL代数的Jacobson根   总被引:1,自引:0,他引:1  
杨有龙  高晓光 《数学学报》2001,44(6):1107-111
Hopenwasser A[1]猜想CSL代数上满足 Ringrose条件的算子集正是它的Jacobson根,Davidson K.R.[2]证明了对于二宽度 CSL代数,上述猜想是完全正确的.本文不仅清楚地刻画了二宽度CSL代数Jacobson根的结构,而且为研究CSL代数的根提供了一种途径.设是由可分Hilbert空间上的套M和N生成的二宽度 CSL,且 W= M∩N;本文得到二宽度 CSL代数的 Jacobson根与套W的根Rw,强根三者之间的一个重要关系同时也给出了真包含Rw的充分必要条件是M≠N且M≠N⊥.  相似文献   

4.
F.A.Szasz在[1]中提出公开问题55:设K是Jacobson根为零的全体亚直既约环类,研究类K确定的上根.本文对此进行了研究,证明了Jacobson根为零的全体亚直既约环类K确定的上根R是特殊根,它介于Jacobson根与Brown-McCoy根之间.并给出任意结合环A为R-根环的充要条件.  相似文献   

5.
51.IntroductionFisher[7]discussedtheHopf-JacobsonradicalJH(A)oftheH--modulealgebraA,whereHisanirreducibleHopfalgebra.In[5],CatgeneralizedFisher'sresult.HeprovedthatJH(A)#HgJ(A#H),whereHisanarbitraryHopfalgebra,AanH--modulealgebra.AversionoftheChevalley-JacobsondensitytheoremforH-modulealgebrawasalsoprovedbyCans].Dually,LiuGuilong[8]definedandstudiedtheHopf-JacobsonradicalofH-comodulealgebraA.Inthispaper,westudyfurthertheHopf-JacobsonradicaloftheH--comodulealgebraA,andwegiveaver…  相似文献   

6.
Stable Jacobson Radicals and Semiprime Smash Products   总被引:1,自引:0,他引:1  
We prove that if H is a finite-dimensional semisimple Hopf algebraacting on a PI-algebra R of characteristic 0, and R is eitheraffine or algebraic over k, then the Jacobson radical of R isH-stable. Under the same hypotheses, we show that the smashproduct algebra R#H is semiprimitive provided that R is H-semiprime.More generally we show that the ‘finite’ Jacobsonradical is H-stable, and that R#H is semiprimitive providedthat R is H-semiprimitive and all irreducible representationsof R are finite-dimensional. We also consider R#H when R isan FCR-algebra. Finally, we prove a general relationship betweenstability of the radical and semiprimeness of R#H; in particularif for a given H, any action of H stabilizes the Jacobson radical,then also any action of H stabilizes the prime radical. 2000Mathematics Subject Classification 16W30, 16N20, 16R99, 16S40.  相似文献   

7.
The Frattini Subalgebra of n-Lie Algebras   总被引:3,自引:0,他引:3  
In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.  相似文献   

8.

We give a quite general construction of irreducible supercuspidal representations and supercuspidal types (in the sense of Bushnell and Kutzko) of -adic groups. In the tame case, the construction should include all known constructions, and it is expected that this gives all supercuspidal representations. We also give a conjectural Hecke algebra isomorphism, which can be used to analyze arbitrary irreducible admissible representations, following the ideas of Howe and Moy.

  相似文献   


9.
This paper is concerned with the connection between the structure space of a locally C*-algebra and the set of its continuous topologically irreducible *-representations. Properties of primitive ideals in such algebras are further investigated, for instance, closed ideals are expressed as intersections of primitive ideals, by using that the Jacobson radical reduces to 0.  相似文献   

10.
In this paper we study the pointed representations of the Virasoro algebra. We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra representations, thus they either are of highest or lowest weights or have all weight spaces of dimension 1. Further, we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights, hence they are also Harish-Chandra representations. This work was supported by CNSF  相似文献   

11.
Abstract Let H be a complex seperable Hilbert space and ~(Jt~) denote the collection of bounded linear operators on H. For an operator in L(H), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.  相似文献   

12.
13.
It is shown that a radical square zero algebra is wild, if and only if it is of Corner’s type, and it is strictly wild if and only if it is Endo-wild. This gives a negative answer to a problem posed by Simson.  相似文献   

14.
In this paper, we consider two approaches toward the definition of a topological prime radical of a topological group. In the first approach, the prime quasi-radical η(G) is defined as the intersection of all closed prime normal subgroups of a topological group G. Its properties are investigated. In the second approach, we consider the set η′(G) of all topologically strictly Engel elements of a topological group G. Its properties are investigated. It is proved that η′(G) is a radical in the class of all topological groups possessing a basis of neighborhoods of the identity element consisting of normal subgroups. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 15–22, 2004.  相似文献   

15.
Representations of Hecke and q-Schur algebras are closely relatedto those of finite general linear groups G in non-describingcharacteristics. Such a relationship can be described by certainfunctors. Using these functors, we determine the Harish-Chandravertices and sources of certain indecomposable G-modules. TheGreen correspondence is investigated in this context. As a furtherapplication of our theory, we establish Steinberg's tensor producttheorems for irreducible representations of G in non-describingcharacteristics. 1991 Mathematics Subject Classification: 20C20,20C33, 20G05, 20G40.  相似文献   

16.
A host algebra of a topological group G is a C *-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C *-algebra C *(S,α), and we describe a setting which permits us to conclude that this C *-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative case is left for the future. To K.H. Hofmann on the occasion of his 75th birthday  相似文献   

17.
We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31: 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.  相似文献   

18.
It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {e ii } I with each ē ii in the center of if Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given. As a corollary, Λ is a finite algebra with non-zero unity element over a perfect field k (e.g., a field with characteristic zero or a finite field) if Λ is isomorphic to a generalized path algebra k (D, Ω, ρ) of finite directed graph with weak relations and dim < ∞; Λ is a generalized elementary algebra which can be lifted with nilpotent Jacobson radical and has a complete set of pairwise orthogonal idempotents if Λ is isomorphic to a path algebra with relations. Presented by Idun Reiten.  相似文献   

19.
Kaiming Zhao 《代数通讯》2013,41(14):4373-4383
In this paper, the weight sets of some irreducible and integrable representations, which are not highest or lowest weight representations, of rank two Kac-Moody algebras of indefinite type are completely determined.  相似文献   

20.
Jan Krempa 《代数通讯》2013,41(1):98-103
We construct a finitely generated monoid S with a zero element such that for every field K the Jacobson radical of the monoid algebra K[S] is a sum of nilpotent ideals but is not nilpotent. Moreover, the contracted monoid algebra K 0[S] is a monomial algebra.

If K is a field of characteristic p > 0, then we construct a finitely presented group H p such that the Jacobson radical J of the group algebra K[H p ] is a sum of nilpotent ideals, but is not nilpotent. Moreover, K[H p ]/J is a domain.  相似文献   

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