摘要:

In this article we give a new technique for exponentiating infinite dimensional graded representations of graded Lie algebras that allows for the exponentiation of some non-locally nilpotent elements. Our technique is to naturally extend the representation of the Lie algebra g on the spaceVnaturally to a representation on a subspace £ of the dual spaceV*. After introducing the technique, we prove that it enables the exponentiation of all elements of free Lie Algebras and afhne Kac-Moody Lie algebras.

ISSN:0092-7872    

DOI:10.1080/00927870008827073

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe the pullback, in the sense of [9], of two Dedekind domains. We describe all those indecomposable pure-injectiveR-modulesMwith finite-dimensional top, that is, such thatM/Rad(R)Mis finite dimensional overR/Rad(R).

ISSN:0092-7872    

DOI:10.1080/00927870008827074

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe an algebra over a fieldk. We say that an idealIofRisco-generatedby a setFofk-linear functionalsR→kifIis the largest ideal ofRthat is contained in the kernels of all the functionals inF;. We will state sufficient conditions for an ideal of a freek-algebra to be co-generated by finitely many functionals. We then get as a corollary that every ideal of the polynomial algebra over a field in finitely many variables is finitely co-generated. This is a known result, but the way we construct the co-generators in the general case, leads to that we get a tight bound on how many co-generators are needed for such ideals.

ISSN:0092-7872    

DOI:10.1080/00927870008827075

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetRbe a ring and ρ a right ideal ofRwith zero right annihilate. Then ρ andRhave the same left Utumi quotient ring. We study the lifting properties of GPIs and some chain conditions inherited by such right ideals. Next, we prove a generalization of Chatters’ theorem. Precisely, we show that ifRis a right nonsingular ring with finite right Goldie dimension and possesses a right ideal ρ such that both ρ andlR(ρ) are PI-rings, then the right Utumi quotient ring ofRis also a Pi-ring.

ISSN:0092-7872    

DOI:10.1080/00927870008827076

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

Following I. Volichenko we study varieties of Lie algebras over a field of characteristic zero, satisfying the identity [[x1,x2,x3], [x4x5x6]] = 0. We prove that the exponential growth of any proper subvariety is a positive integer and any positive integer can be so realized.

ISSN:0092-7872    

DOI:10.1080/00927870008827077

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

In this note, we give a necessary and sufficient condition for a real irreducible representation of a real simple Lie algebra to admit an invariant bilinear form. We also determine when the invariant bilinear form is symmetric or skew-symmetric.

ISSN:0092-7872    

DOI:10.1080/00927870008827078

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008827079

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We show that outer ideals of Jordan algebras, pairs and triple systems inherit nondegeneracy, strong primeness and primitivity.

ISSN:0092-7872    

DOI:10.1080/00927870008827080

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetXbe a smooth complex projectiven-fold endowed with an ample and spanned line bundle (L). Under the assumption that Γ(L) defines a generically one-to-one map we describe the singular set of the general element in the main component of the discriminant locus of |L|. This description is used to show that (X:,L) is covered by linear Pk’s, wherek+ 1 stands for the codimension of the main component. We also give some applications relating k to the spectral value of (X, L) and discuss some examples.

ISSN:0092-7872    

DOI:10.1080/00927870008827081

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

On étudie le groupe affine 𝔊 correspondant à I’algèbre de battage de Hopf, et on montre que tout groupe algébrique unipotent est un quotient de 𝔊. De plus, on utilise 𝔊 pour mieux comprendre quelques caractérisations des séries de Lie en termes de battages.

ISSN:0092-7872    

DOI:10.1080/00927870008827082

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor