共查询到20条相似文献,搜索用时 15 毫秒
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Frederik Caenepeel 《代数通讯》2018,46(11):4985-5005
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Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V)?=?V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations of the solvable Lie algebra 𝔤?=??x??L(V), where x acts on V via an arbitrary invertible Jordan block. 相似文献
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Thierry Levasseur 《Proceedings of the American Mathematical Society》2002,130(12):3519-3523
Let be a complex semisimple Lie algebra and be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of is equal to the dimension of a Borel subalgebra of .
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E. Horozov 《Bulletin des Sciences Mathématiques》2002,126(7):605-614
In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc). 相似文献
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Grant F. Armstrong Grant Cairns Barry Jessup 《Proceedings of the American Mathematical Society》1997,125(2):381-385
Betti numbers for the Heisenberg Lie algebras were calculated by Santharoubane in his 1983 paper. However few other examples have appeared in the literature. In this note we give the Betti numbers for a family of -dimensional 2-step nilpotent extensions of by .
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We describe degenerations of four-dimensional binary Lie algebras, and five- and six-dimensional nilpotent Malcev algebras over ?. In particular, we describe all irreducible components of these varieties. 相似文献
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Peyman Niroomand 《Linear and Multilinear Algebra》2013,61(8):831-836
For every finite p-group G of order p n with derived subgroup of order p m , Rocco [N.R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. 1 (1991), pp. 63–79] proved that the order of tensor square of G is at most p n(n?m). This upper bound has been improved recently by the author [P. Niroomand, On the order of tensor square of non abelian prime power groups (submitted)]. The aim of this article is to obtain a similar result for a non-abelian nilpotent Lie algebra of finite dimension. More precisely, for any given n-dimensional non-abelian nilpotent Lie algebra L with derived subalgebra of dimension m we have dim(L???L)?≤?(n???m)(n???1)?+?2. Furthermore for m?=?1, the explicit structure of L is given when the equality holds. 相似文献
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András Domokos Roland EsquerraBob Jaffa Tom Schulte 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4642-4652
In this paper, we consider a natural subelliptic structure in semisimple, compact and connected Lie groups, and estimate the constant in the so-called subelliptic Friedrichs-Knapp-Stein inequality, which has implications in the regularity theory of p-energy minimizers. 相似文献
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A new characterization of semisimple Lie algebras 总被引:4,自引:0,他引:4
Said Benayadi 《Proceedings of the American Mathematical Society》1997,125(3):685-688
Using Casimir elements, we characterize the semisimple Lie algebras among the quadratic Lie algebras. This characterization gives, in particular, a generalization of a consequence of Cartan's second criterion.
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Let be a non-abelian, connected, simply connected, nilpotent Lie group. We show that the eigenvectors of a finite number of families
of left invariant differential operators and their conjugates span a dense subspace of L
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(G). The restriction of the left regular representation to each one of these (left invariant) eigenspaces disintegrates into
irreducible unitary representations with multiplicities 0 and 1 only.
J. Ludwig and C. Molitor-Braun are supported by the research grant R1F104C09 of the University of Luxembourg. 相似文献
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Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let Ln(V) denote the nth homogeneous component of the free Lie algebra on V. We study the structure of Ln(V) as a module for the general linear group GLr(F) when n=pk and k is not divisible by p and where r≥n. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of
Lk(V) and the indecomposable direct summands of Ln(V) which are not isomorphic to direct summands of V⊗n. Our approach uses idempotents of the Solomon descent algebras, and in addition a correspondence theorem for permutation
modules of symmetric groups.
Second author supported by Deutsche Forschungsgemeinschaft (DFG-Scho 799). 相似文献
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Ignacio Bajo 《Geometriae Dedicata》1997,66(3):281-291
Lie groups with bi-invariant semi-Riemannian metrics are considered. We study the decomposition of the algebra of prederivations of a direct sum of Lie algebras and derive some results on the isotropy group of a bi-invariant product Lie group. We also give necessary and sufficient conditions to ensure that all isometries of a complex Lie group, endowed with a bi-invariant Norden metric, are holomorphic. 相似文献