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Anselm Eggert 《Semigroup Forum》1990,41(1):115-121
This paper gives some basic facts on Lie semialgebras and shows the crucial steps that lead to a classification of semialgebras
in a class of Lie algebras that contains the reductive ones. The classification of invariant wedges by Hilgert and Hofmann
is a prerequisite.
This paper was presented at the Conference on “The analytical and topological theory of semigroups” in Oberwolfach, January
29 through February 4, 1989 相似文献
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Emmanuel Letellier 《Journal of Algebra》2009,321(6):1696-1710
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We classify all (finitely dimensional) nilpotent Lie k-algebras h with 2-dimensional commutator ideals h′, extending a known result to the case where h′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h′ is central, it is independent of k if h′ is non-central and is uniquely determined by the dimension of h. In the case where k is algebraically or real closed, we also list all nilpotent Lie k-algebras h with 2-dimensional central commutator ideals h′ and dimkh?11. 相似文献
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Let G and H be Lie groups with Lie algebras
and
. Let G be connected. We prove that a Lie algebra homomorphism
is exact if and only if it is completely positive. The main resource is a corresponding theorem about representations on
Hilbert spaces.
This article summarizes the main results of [1].
Received: 6 December 2005 相似文献
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M. V. Zaitsev 《Mathematical Notes》1989,45(6):469-472
Translated from Matematicheskie Zametki, Vol. 45, No. 6, pp. 56–60, June, 1989. 相似文献
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Let G be a reductive group over a field k of characteristic ≠2, let , let θ be an involutive automorphism of G and let be the associated symmetric space decomposition. For the case of a ground field of characteristic zero, the action of the isotropy group Gθ on is well understood, since the well-known paper of Kostant and Rallis [B. Kostant, S. Rallis, Orbits and representations associated with symmetric spaces, Amer. J. Math. 93 (1971) 753–809]. Such a theory in positive characteristic has proved more difficult to develop. Here we use an approach based on some tools from geometric invariant theory to establish corresponding results in (good) positive characteristic.Among other results, we prove that the variety of nilpotent elements of has a dense open orbit, and that the same is true for every fibre of the quotient map . However, we show that the corresponding statement for G, conjectured by Richardson, is not true. We provide a new, (mostly) calculation-free proof of the number of irreducible components of , extending a result of Sekiguchi for . Finally, we apply a theorem of Skryabin to describe the infinitesimal invariants . 相似文献
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M. V. Zaitsev 《Algebra and Logic》1998,37(4):223-233
A variety of Lie algebras over a field of characteristic 0 has a finite superrank if it is generated by the Grassmann envelope
of a finitely generated Lie superalgebra. We prove that every commutator variety not in NcA has infinite superrank. Consequently, infinite are superranks of all polynilpotent varieties of Lie algebras except Nc and NcA.
Supported by RFFR grant No. 96-01-00146.
Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 394–412, July–August. 1998. 相似文献
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Yu. A. Bakhturin 《Mathematical Notes》1968,4(4):725-730
The varieties of Lie algebras in which every subalgebra of the free algebra is also free are completely described, and a proof is given for a theorem on the verbal ideals of the ideals of an absolutely free Lie algebra.Translated from Matematicheskie Zametki, Vol. 4, No. 4, pp. 389–398, October, 1968.The author takes this opportunity to thank A. L. Shmel'kin for suggesting the proof of the analog of the Neumann-Weigold theorem for varieties of Lie algebras. 相似文献