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1. CMB Online first
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras |
On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras We describe of all finite
dimensional uniserial representations of a commutative associative
(resp. abelian Lie) algebra over a perfect (resp. sufficiently
large perfect) field. In the Lie case the size of the field
depends on the answer to following question, considered and solved
in this paper. Let $K/F$ be a finite separable field extension
and
let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some
non-zero elements $\alpha,\beta\in F$?
Keywords:uniserial module, Lie algebra, associative algebra, primitive element Categories:17B10, 13C05, 12F10, 12E20 |
2. CMB 2012 (vol 56 pp. 606)
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 |
3. 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 |
4. 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 |
5. 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 |
6. 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 Categories:17B05, 17B65 |
7. 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 |