1. CMB Online first
|Characterization of Simple Highest Weight Modules|
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
Keywords:Lie algebra, highest weight module, triangular decomposition, locally nilpotent action
Categories:17B20, 17B65, 17B66, 17B68
2. CMB 2011 (vol 55 pp. 579)
|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
3. CMB 2011 (vol 54 pp. 442)
|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
4. CMB 2011 (vol 54 pp. 472)
|A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps|
We study infinitesimal deformations of holomorphic maps of compact, complex, KÃ¤hler 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
5. CMB 2008 (vol 51 pp. 298)
|The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras |
In this paper we prove that the Kostrikin radical of an extended affine Lie algebra of reduced type coincides with the center of its core, and use this characterization to get a type-free description of the core of such algebras. As a consequence we get that the core of an extended affine Lie algebra of reduced type is invariant under the automorphisms of the algebra.
Keywords:extended affine Lie algebra, Lie torus, core, Kostrikin radical
6. CMB 2000 (vol 43 pp. 3)
|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