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1.
Rutwig Campoamor-Stursberg 《Journal of Mathematical Sciences》2007,144(5):4423-4430
In this work, we enlarge the definition of products by generators of Lie algebras to the class of solvable Lie algebras. We
analyze the number of independent invariant functions for the coadjoint representation of these algebras by means of the Maurer-Cartan
equations and give some applications to product structures on Lie algebras.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 85–94, 2005. 相似文献
2.
Jeanne Erdman Snow 《manuscripta mathematica》1990,66(1):397-412
In this paper, invariant complex structures on four-dimensional, solvable, simply-connected real Lie groups are classified
where the dimension of the commutator is less than three. The resulting complex surfaces corresponding to these structures
are also determined. The classification problem is reduced to determining certain complex “structure” subalgebras of the complexifications
of the four-dimensional, solvable real Lie algebras. Most of the eleven types of non-abelian solvable real Lie algebras do
have complex structure subalgebras; three do not. Only three types of algebras have solvable complex structure subalgebras,
and only one possesses both abelian and solvable complex structure subalgebras. Each of the possible homogeneous surfaces
is represented in the list of resulting manifolds. 相似文献
3.
V. D. Lyakhovskii 《Journal of Mathematical Sciences》1997,83(1):106-112
A wide class of quantum universal enveloping algebras uniquely corresponding to Hopf algebras H with spectrum Q(H) in the
category of groups is defined. Such quantum algebras are the quantum groups of the simply connected solvable Lie groups P(H).
Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 168–178
Translated by V. D. Lyakhovskii 相似文献
4.
A. V. Mikhalev I. N. Balaba S. A. Pikhtilkov 《Journal of Mathematical Sciences》2008,149(2):1146-1156
In this paper, we introduce the class of graded Ω-groups, which includes: groups; associative, conformal and vertex algebras;
Lie algebras and graded algebras. The graded prime radical of a graded Ω-group is defined, and its elementwise characterization
is given. It is shown that the graded prime radical of a graded Ω-groups with a finiteness condition coincides with the lower
weakly solvable (in the Parfyonov sense) radical.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 159–174, 2006. 相似文献
5.
A. M. Meirmanov 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):204-213
We study applications of a new class of infinite-dimensional Lie algebras, called Lax operator algebras, which goes back to the works by I. Krichever and S. Novikov on finite-zone integration related to holomorphic vector bundles
and on Lie algebras on Riemann surfaces. Lax operator algebras are almost graded Lie algebras of current type. They were introduced
by I. Krichever and the author as a development of the theory of Lax operators on Riemann surfaces due to I. Krichever, and
further investigated in a joint paper by M. Schlichenmaier and the author. In this article we construct integrable hierarchies
of Lax equations of that type.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 216–226.
Dedicated to S.P. Novikov on the occasion of his 70th birthday 相似文献
6.
It is proved that the colength of every API-variety of Lie algebras grows polynomially, and we give a number of examples in
which the colength grows more rapidly than any polynomial function does. These indicate that for many of the important varieties
of Lie algebras, such as varieties of solvable algebras of derived length 3, varieties generated by some infinite-dimensional
simple algebras of Cartan type, or by certain Katz-Mudi algebras, the growth of colength will be superpolynomial.
Supported by RFFR grants No. 96-01-00146 and No. 96-15-96050.
Translated fromAlgebra i Logika, Vol. 38, No. 2, pp. 161–175, March–April, 1999. 相似文献
7.
A. P. Petravchuk 《Ukrainian Mathematical Journal》1999,51(5):707-715
We consider a Lie algebraL over an arbitrary field that is decomposable into the sumL=A+B of an almost Abelian subalgebraA and a subalgebraB finite-dimensional over its center. We prove that this algebra is almost solvable, i.e., it contains a solvable ideal of
finite codimension. In particular, the sum of the Abelian and almost Abelian Lie algebras is an almost solvable Lie algebra.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 636–644, May, 1999. 相似文献
8.
We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of the Lie algebraic
approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic, then
the corresponding base manifolds are necessarily diffeomorphic. Further, we give two characterizations of the isomorphisms
of the Lie algebras of sections for Atiyah algebroids associated to principal bundles with semisimple structure groups. For
instance we prove that in the semisimple case the Lie algebras of sections are isomorphic if and only if the corresponding
Lie algebroids are, or, as well, if and only if the integrating principal bundles are locally isomorphic. Finally, we apply
these results to describe the isomorphisms of sections in the case of reductive structure groups—surprisingly enough they
are no longer determined by vector bundle isomorphisms and involve dive rgences on the base manifolds. 相似文献
9.
Sh. M. Kasymov 《Algebra and Logic》1995,34(3):147-154
It is shown that Cartan's criteria for finite-dimensional Lie algebras to be semisimple and solvable are fully adaptable to
n-Lie algebras, provided that ideals of an n-Lie algebra are understood to be solvable in the sense of Kuz'min. Specifically,
we present a characterization of the Kuz'min radical in terms of a trace form associated with some representation ρ, which
is analogous to the characterization which we have in the case of Lie algebras. One more analog of the Cartan theorem is proved
for n-Lie algebras which are solvable in the sense of Filippov.
Translated fromAlgebra i Logika, Vol. 34, No. 3, pp. 274-287, May-June, 1995. 相似文献
10.
M. V. Zaitsev 《Mathematical Notes》1997,62(1):80-86
In this paper the identities of the complex affine Kac-Moody algebras are studied. It is proved that the identities of twisted
affine algebras coincide with those of the corresponding nontwisted algebras. Moreover, in the class of nontwisted affine
Kac-Moody algebras, each of these algebras is uniquely defined by its identities. It is shown that the varieties of affine
algebras, as well as the varieties defined by finitely generated three-step solvable Lie algebras, have exponential growth.
Translated fromMatematicheskie Zametki, Vol. 62 No. 1, pp. 95–102, July 1997.
Translated by A. I. Shtern 相似文献
11.
We continue to investigate strongly and weakly Lie remarkable equations, which we defined in a recent paper. We consider some
relevant algebras of vector fields on ℝk (such as the isometric, affine, projective, or conformal algebras) and characterize strongly Lie remarkable equations admitted
by the considered Lie algebras.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 486–494, June, 2007. 相似文献
12.
13.
Francesco Catino Salvatore Siciliano Ernesto Spinelli 《Algebras and Representation Theory》2010,13(6):653-660
Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503–513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ⌈log2(p + 1)⌉. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this
lower bound. 相似文献
14.
A. Gangopadhyaya J. V. Mallow C. Rasinariu U. P. Sukhatme 《Theoretical and Mathematical Physics》1999,118(3):285-294
Analytic expressions for the eigenvalues and eigenfunctions of nonrelativistic shape-invariant Hamiltonians can be derived
using the well-known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum-generating
algebras and are hence solvable by an independent group theory method. We demonstrate the equivalence of the two solution
methods by developing an algebraic framework for shape-invariant Hamiltonians with a general parameter change involving nonlinear
extensions of Lie algebras.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 362–374, March, 1999. 相似文献
15.
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp(T) and Ф(T) for solvable Lie triple systems. 相似文献
16.
We introduce the notion of radical in Bernstein algebras and prove a splitting theorem, that is an analog of a well-known statement in classical varieties of algebras. Note that in this situation Bernstein algebras are more similar to solvable Lie and Malcev algebras (see [4], [6]) than to associative, Jordan or Binary Lie ones. Throughout the paper all algebras and vector spaces are finite dimensional over an algebraically closed field k of characteristic 0. 相似文献
17.
The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥?V, where 𝔥?𝔤𝔩(V), |dim V?dim 𝔤|≤1 and NilRad(𝔤) = V, V being a finite dimensional vector space. In particular, it is proved that every complex Frobenius solvable Lie algebra is decomposable, whereas that in the real case there are only two indecomposable Frobenius solvable Lie algebras. 相似文献
18.
We define a class of infinite-dimensional Lie algebras that generalize the universal enveloping algebra of the algebra sl(2,
ℂ) regarded as a Lie algebra. These algebras are a special case of ℤ-graded Lie algebras with a continuous root system, namely,
their Cartan subalgebra is the algebra of polynomials in one variable. The continuous limit of these algebras defines new
Poisson brackets on algebraic surfaces.
In memory of M. V. Saveliev
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 345–352, May, 2000. 相似文献
19.
J. V. Kochetova 《Journal of Mathematical Sciences》2010,166(5):661-669
The concept of the lower weakly solvable radical of Lie algebras is important in the study of Lie algebras. The purpose of
this paper is to investigate the generalization of this concept to lattice ordered Lie algebras over partially ordered fields.
Some results concerning properties of the lower weakly solvable l-radical of lattice ordered Lie algebras are obtained. Necessary and sufficient conditions for the l-prime radical of a Lie l-algebra to be equal to the lower weakly solvable l-radical of the Lie l-algebra are presented. 相似文献
20.
We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras
which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras
defined over fields of characteristic zero are now known in principle.
Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002 相似文献