ISSN:0092-7872    

DOI:10.1080/00927879408824896

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

We examine two problems in the computational theory of Lie algebras. First, we prove a constructive version of Engel's theorem: if L is a finite-dimensional Lie algebra that is not nilpotent, we show how to construct an element x in L such that the linear transformation ad x is not nilpotent. No special assumptions about the underlying field are needed. Second, as an important application of the first result, we give an algorithm for the construction of a Cartan subalgebra of a finite-dimensional Lie algebra. This solves the problem of finding a totally constructive proof of the existence of a Cartan subalgebra, posed by Beck, Kolman, and Stewart in the paper "Computing the Structure of a Lie Algebra". Our proofs are ordinary mathematical proofs that do not employ the general law of excluded middle. The advantage of this approach to mathematics is that our proofs, which are not burdened or obscured by the details of a particular programming language, can nevertheless be routinely turned into computer programs

ISSN:0092-7872    

DOI:10.1080/00927879408824897

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824898

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824899

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824900

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824901

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

In this note we investigate the length of a strictly descending chain of maximum length in simple groups of Lie type in odd characteristic p. We desire information regarding which maximal subgroups can support (serve as the initial proper step in a longest chain) a longest chain in in G. Considered herein are those M possessing a simple Generalized Fitting subgroup. We show that if M supports a longest chain and has length exceeding that of every maximal parabolic subgroup of G, then either F*(M) is a Lie type group in the same characteristic as C, or Alt(5) = F*(M) = M and G≌L2(p)

ISSN:0092-7872    

DOI:10.1080/00927879408824902

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824903

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

摘要:

The formula dim(A+B)=dim(A)+dim(B)-dim(A∩B) works when ‘dim’ stands for the dimension of subspaces A,B of any vector space. In general, however, it does no longer hold if 'dim' means the uniform (or Goldie) dimension of submodules A,B of a module M over a ring R, and in fact the left hand side may be infinite while the right hand side is finite. In this paper we shall give a characterization of those modules M in which the formula holds for any two submodules A,B, as well as some conditions in the ring R which guarantee that dim(A+B) is finite whenever A and B are finite dimensional R-modules.

ISSN:0092-7872    

DOI:10.1080/00927879408824904

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927879408824905

出版商:Marcel Dekker, Inc.    

年代:1994

数据来源: Taylor