Results 151 to 160 of about 277 (187)

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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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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On nilpotent Lie algebras

Algebra and Logic, 1971
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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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Nilpotent Lie Algebras.

1961
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/184753/2/6106327 ...
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On the nilpotency and decomposition of Lie-type algebras

Mathematical Notes, 2007
Let \(G\) be a semigroup acting on a set \(M\). Consider a \(G\)-graded algebra \(B\) over a field \(k\), not necessarily associative, and an \(M\)-graded space \(V\). A Lie-type representation of \(B\) in \(V\) is a linear map \(\rho\) from \(B\) into the endomorphism algebra of \(V\) such that \(\rho(B_\alpha)V_\gamma\subseteq V_{\alpha\gamma}\), and
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ON THE RATIONAL FORMS OF NILPOTENT LIE ALGEBRAS AND LATTICES IN NILPOTENT LIE GROUPS

2002
Let \(L\) be a real finite-dimensional nilpotent Lie algebra and \(H\) be a rational subalgebra of \(L\). \(H\) is called a rational form for \(L\) if there exists a basis of \(H\) over \(Q\) which is also a real basis for \(L\). Rational forms for the Lie algebra of a nilpotent Lie group give rise to lattices in the group.
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