Results 171 to 180 of about 538,257 (210)

Degenerations of Nilpotent Lie Algebras

Journal of Lie Theory, 1999
Summary: In this paper we study degenerations of nilpotent Lie algebras. If \(\lambda,\mu\) are two points in the variety of nilpotent Lie algebras, then \(\lambda\) is said to degenerate to \(\mu\), \(\lambda \rightarrow_{\text{deg}} \mu\), if \(\mu\) lies in the Zariski closure of the orbit of \(\lambda\).
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Characteristically nilpotent Lie algebras

Algebra and Logic, 1989
The author gives a big class of characteristically nilpotent Lie algebras in any dimension \(\geq 15\) and discusses their geometric interpretation.
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Derivation Algebras of Certain Nilpotent Lie Algebras

Journal of Lie Theory, 2001
Let \(L\) be a nilpotent Lie algebra and for \(x\in L\), \(\text{ad}(x): y\mapsto [x,y]\) for all \(y\in L\) the adjoint operator. For all \(x\in L-[L,L]\), let \(c(x)= (c_1(x), c_1(x),\dots, 1)\) be the sequence, in decreasing order of the characteristic subspaces of the nilpotent operator \(\text{ad}(x)\).
Cabezas, J. M., Gómez, J. R.
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On nilpotent Lie algebras

Algebra and Logic, 1971
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lie-Nilpotency Indices of Group Algebras

Bulletin of the London Mathematical Society, 1992
For an associative ring \(A\), define \(A^{[1]}\) to be \(A\) and \(A^{[n]}\) (\(n>1\)) to be the two-sided ideal of \(A\) that is generated by all \(n\)- fold Lie commutators \([a_ 1,[a_ 2,\dots,[a_{n-1},a_ n]\dots]]\) (\(a_ i\in A\)). \(A\) is called Lie-nilpotent if \(A^{[n]}=0\) for some \(n\), in which case the smallest such \(n\) is denoted \(t_ ...
Bhandari, Ashwani K., Passi, I. B. S.
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On derivatives of nilpotent Lie algebras

1998
The classification problem of solvable Lie algebras is still open. One of its important points is to decide for a given nilpotent Lie algebra whether or not it is the nilpotent radical of any solvable Lie algebra. The authors prove some results in this direction. Namely, using the known classifications of the nilpotent Lie algebras of small dimensions,
Barbari, P., Kobotis, A.
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Nilpotent Lie Algebras and Solvable Lie Algebras

1987
The Lie algebras considered in this chapter are finite-dimensional algebras over a field k. In Sees. 7 and 8 we assume that k has characteristic 0. The Lie bracket of x and y is denoted by [x, y], and the map y → [x, y] by ad x.
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Associative and Jordan Lie Nilpotent Algebras

Algebra and Logic, 2023
Let \(\Phi\) be a commutative associative unital ring where the element 6 is invertible, and consider algebras over \(\Phi\). Let \(u=u_3 = (x_1,x_2,x_3)\) be the associator of three variables in the free Jordan algebra, and denote by \(u_{2n+1} = (u_{2n-1}, x_{2n}, x_{2n+1})\) the (left-normed) associator of length \(2n+1\).
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On Holomorphic Realizations of Nilpotent Lie Algebras

Functional Analysis and Its Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akopyan, R. S., Loboda, A. V.
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Subquotients in the Enveloping Algebra of a Nilpotent Lie Algebra

Journal of Lie Theory, 2001
Let \(G\) be a connected simply connected nilpotent real Lie group, \(H\) an analytic subgroup of \(G\) and \(\chi\) a unitary character of \(H\). Let \(\tau= \text{Ind}_H^G\chi\). Then the conjecture of Duflo-Corwin-Greenleaf states that the algebra \(D_\tau(G/H)\) of \(C^{\infty}\) \(G\)-invariant differential operators on the space \(G/H\) is ...
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