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Results 1 - 4 of 4 |
1. CMB 2011 (vol 55 pp. 579)
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Casimir Operators and Nilpotent Radicals It is shown that a Lie algebra having a nilpotent radical has a
fundamental set of invariants consisting of Casimir operators. A
different proof is given in the well known special case of an
abelian radical. A result relating the number of invariants to the
dimension of the Cartan subalgebra is also established.
Keywords:nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariants Categories:16W25, 17B45, 16S30 |
2. CMB 2011 (vol 54 pp. 442)
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Nondegeneracy for Lie Triple Systems and Kantor Pairs We study the transfer of nondegeneracy
between Lie triple systems and their standard Lie algebra envelopes
as well as between Kantor pairs, their associated Lie triple systems,
and their Lie algebra envelopes. We also show that simple Kantor
pairs and Lie triple systems in characteristic $0$ are
nondegenerate.
Keywords:Kantor pairs, Lie triple systems, Lie algebras Categories:17A40, 17B60, 17B99 |
3. CMB 2011 (vol 54 pp. 472)
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A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps We study infinitesimal deformations of holomorphic maps of
compact, complex, Kähler manifolds. In particular, we describe a
generalization of Bloch's semiregularity map that annihilates
obstructions to deform holomorphic maps with fixed codomain.
Keywords:semiregularity map, obstruction theory, functors of Artin rings, differential graded Lie algebras Categories:13D10, 14D15, 14B10 |
4. CMB 2000 (vol 43 pp. 3)
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Resolutions of Associative and Lie Algebras Certain canonical resolutions are described for free associative and
free Lie algebras in the category of non-associative algebras. These
resolutions derive in both cases from geometric objects, which in turn
reflect the combinatorics of suitable collections of leaf-labeled
trees.
Keywords:resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron Categories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50 |