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1.
We exhibit a class of Lie algebras (which contains, in particular, free polynilpotent Lie algebras) that have wild automorphisms, i.e., automorphisms which are not induced by automorphisms of a free Lie algebra.  相似文献   

2.
李昭  曾波  曹佑安 《数学学报》2012,(5):811-816
设A为交换变元x_1,x_2的罗朗多项式代数,记A的导子代数Der A为M.本文确定了A,M的对合自同构.利用M的对合自同构给出了一类无限维单李三系,并且通过讨论M的自同构与对合自同构的关系,确定这些单李三系的自同构.  相似文献   

3.
Given a norm on a finite dimensional vector space V, we may consider the group of all linear automorphisms which preserve it. The Lie algebra of this group is a Lie subalgebra of the endomorphism algebra of V having two properties: (1) it is the Lie algebra of a compact subgroup, and (2) it is “saturated” in a sence made precise below. We show that any Lie subalgebra satisfying these conditions is the Lie algebra of the group of linear automorphisms preserving some norm. There is an appendix on elementary Lie group theory.  相似文献   

4.
Let K be an associative commutative ring with identity, and let R be the algebra of lower niltriangular n × n matrices over K. For n = 3, we prove that local automorphisms and Lie automorphisms of the algebra R generate all its local Lie automorphisms. For the case when K is a field and n = 4, we describe local automorphisms, local derivations, and local Lie automorphisms of the algebra R.  相似文献   

5.
Schur showed that if the center of a group has finite index, then the commutator subgroup is finite. By replacing inner automorphisms by automorphisms, Hegarty obtained a variation of Schur's result. The Lie algebra analogue of Schur's result is well-known. We obtain a strong Lie algebra version of Hegarty's result.  相似文献   

6.
构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.  相似文献   

7.
Over an algebraically closed field of characteristic zero simple Lie algebras admit outer automorphisms of order 3 if and only if they are of type D4. Moreover, thereare two conjugacy classes of such automorphisms. Among orthogonal Lie algebras over arbitrary fields of characteristic zero, only orthogonal Lie algebras relative to quadratic norm forms of Cayley algebras admit outer automorphisms of order 3. We give a complete list of conjugacy classes of outer automorphisms of order 3 for orthogonal Lie algebras over arbitrary fields of characteristic zero. For the norm form of a given Cayley algebra, one class is associated with the Cayley algebra and the others with central simple algebras of degree 3 with involution of the second kind such that the cohomological invariant of the involution is the norm form.  相似文献   

8.
张建华  曹怀信 《数学学报》2004,47(1):119-124
本文引入了Banach代数上线性映射的Lie不变子空间,给出了因子VonNeumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一般形式,研究了Lie导子与Lie自同构的概念及了Lie导子与Lie自同构半群的关系.  相似文献   

9.
《代数通讯》2013,41(4):1639-1647
We prove that the group of tame automorphisms of the universal enveloping algebra of the three-dimensional nilpotent nonabelian Lie algebra over a field of characteristic 0 is dense with respect to the formal power series topology in the group of all automorphisms.

  相似文献   

10.
Eric Müller 《代数通讯》2013,41(2):1029-1044
We compute the coradical filtration and the group of Hopf algebra automorphisms of the non-restricted specialization of the quantized universal enveloping algebra of a finite-dimensional semisimple Lie algebra.  相似文献   

11.
We define a class of derivations on the algebra of the non-commutative power series in two variables and study the structure of the Lie algebra generated by them. After detecting the corresponding automorphisms under the exponential map explicitly, we clarify the structure of the automorphism group by means of the Hausdorff group associated to the Lie algebra.  相似文献   

12.
The only known examples of Anosov diffeomorphisms are hyperbolic automorphisms of infranilmanifolds, and the existence of such automorphisms is a really strong condition on the rational nilpotent Lie algebra determined by the lattice, so called an Anosov Lie algebra. We prove that n⊕?⊕n (s times, s≥2) has an Anosov rational form for any graded real nilpotent Lie algebra n having a rational form. We also obtain some obstructions for the types of nilpotent Lie algebras allowed, and use the fact that the eigenvalues of the automorphism are algebraic integers (even units) to show that the types (5,3) and (3,3,2) are not possible for Anosov Lie algebras.  相似文献   

13.
Nonlinearity of the Automorphism Groups of Some Free Algebras   总被引:2,自引:2,他引:0  
We prove that the groups of tame automorphisms of a free Lie algebra (free associative algebra, absolutely free algebra, algebra of polynomials) of rank at least four over a field of characteristic zero admit no faithful representation by matrices over any field.  相似文献   

14.
We describe the hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra over an arbitrary field. Using it, we prove that this group admits no faithful representation by matrices over a field provided that the algebra rank is at least four.  相似文献   

15.
In this paper, automorphisms of the algebra ofq-difference operators, as an associative algebra for arbitraryq and as a Lie algebra forq being not a root of unity, are determined. Project supported by the NNSF of China  相似文献   

16.
We show that an algebra with a non-nilpotent Lie group of automorphisms or “symmetries” (e.g., smooth functions on a manifold with such a group of diffeomorphisms) may generally be deformed (in the function case, “quantized”) in such a way that only a proper subgroup of the original group acts. This symmetry breaking is a consequence of the existence of certain “universal deformation formulas” which are elements, independent of the original algebra, in the tensor algebra of the enveloping algebra of the Lie algebra of the group.  相似文献   

17.
Let X be a JB-algebra without spin factor representation of dimension 3. It is shown that the Banach Lie algebra aut(X) of all derivations of X is semi-simple, and aut(X) is (topologically) simple if X is simple. This extends results of Jacobson and Meyberg to the infinite dimensional case. Applications to the Lie algebra of all infinitesimal automorphisms of a symmetric Banach tube domain are given.Research supported by the Deutsche Forschungsgemeinschaft  相似文献   

18.
The double Lie algebra LD of rooted trees decorated by a set D is introduced, generalising the construction of Connes and Kreimer. It is shown that it is a simple Lie algebra. Its derivations and its automorphisms are described, as well as some central extensions. Finally, the category of lowest weight modules is introduced and studied.  相似文献   

19.
Khanmamedov  A. Kh.  Mamedova  A. F. 《Mathematical Notes》2022,111(1-2):281-288
Mathematical Notes - A criterion is given for the Lie algebra of infinitesimal holomorphic automorphisms of the direct product of two germs of real analytic generic CR manifolds to be equal to the...  相似文献   

20.
《代数通讯》2013,41(9):4139-4155
In the paper we present an extension of Segal theorem on Lie algebra automorphisms of upper triangular nilpotent matrices to the whole class of nilpotent subalgebras generated by positive parts of indecomposable Chevalley algebras.  相似文献   

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