Updated: 2012-08-31 16:52:48
Contact us Help Shopping cart Home About us Article title , keywords or abstract Article title Publication title Author Advanced search Subject Publisher Publication Browse : by Home The Journal of Management Development Volume 31, Number 8 A thematic analysis of a leadership speaker series Authors : Hartman , Nathan S . Conklin , Thomas : Source The Journal of Management Development Volume 31, Number 8, 2012 pp . 826-844(19 Publisher : Emerald Group Publishing Limited view table of contents next article Buy download fulltext : article OR Pressing the buy now button more than once may result in multiple purchases Price : 38.00 plus tax Refund Policy : Abstract : Keywords Career guidance Leadership Leadership development Lectures Mixed methods Senior management Students Thematic analysis
Updated: 2012-08-30 01:07:53
Now that we’ve given the proof, we want to mention a few uses of the Jordan-Chevalley decomposition. First, we let be any finite-dimensional -algebra — associative, Lie, whatever — and remember that contains the Lie algebra of derivations . I say that if then so are its semisimple part and its nilpotent part ; it’s [...]
Updated: 2012-08-28 20:38:29
We now give the proof of the Jordan-Chevalley decomposition. We let have distinct eigenvalues with multiplicities , so the characteristic polynomial of is We set so that is the direct sum of these subspaces, each of which is fixed by . On the subspace , has the characteristic polynomial . What we want is a [...]
Updated: 2012-08-28 01:16:24
We recall that any linear endomorphism of a finite-dimensional vector space over an algebraically closed field can be put into Jordan normal form: we can find a basis such that its matrix is the sum of blocks that look like where is some eigenvalue of the transformation. We want a slightly more abstract version of [...]
Updated: 2012-08-25 21:18:23
We’d like to have matrix-oriented versions of Engel’s theorem and Lie’s theorem, and to do that we’ll need flags. I’ve actually referred to flags long, long ago, but we’d better go through them now. In its simplest form, a flag is simply a strictly-increasing sequence of subspaces of a given finite-dimensional vector space. And we [...]
Updated: 2012-08-25 21:17:06
The lemma leading to Engel’s theorem boils down to the assertion that there is some common eigenvector for all the endomorphisms in a nilpotent linear Lie algebra on a finite-dimensional nonzero vector space . Lie’s theorem says that the same is true of solvable linear Lie algebras. Of course, in the nilpotent case the only [...]
Updated: 2012-08-25 16:15:22
In some respects, life continues to move slowly, as it has for the past few weeks. I’ve been focused on Heaviside’s operational calculus for differential equations. For some reason, I failed to find this material in the book I bought for the purpose… but I found it on a 2nd look, and it has been [...]
Updated: 2012-08-22 22:34:53
When we say that a Lie algebra is nilpotent, another way of putting it is that for any sufficiently long sequence of elements of the nested adjoint is zero for all . In particular, applying enough times will eventually kill any element of . That is, each is ad-nilpotent. It turns out that the converse [...]
Updated: 2012-08-22 15:39:49
Bill Thurston passed away yesterday at 8pm, succumbing to the cancer that he had been battling for the past two years. I don’t think it’s possible to overstate the revolutionary impact that he had on the study of geometry and topology. Almost everything we blog about here has the imprint of his amazing mathematics. [...]
Updated: 2012-08-21 12:59:50
Solvability is an interesting property of a Lie algebra , in that it tends to “infect” many related algebras. For one thing, all subalgebras and quotient algebras of are also solvable. For the first count, it should be clear that if then . On the other hand, if is a quotient epimorphism then any element [...]
Updated: 2012-08-20 22:46:02
There are two big types of Lie algebras that we want to take care of right up front, and both of them are defined similarly. We remember that if and are ideals of a Lie algebra , then — the collection spanned by brackets of elements of and — is also an ideal of . [...]
Updated: 2012-08-18 20:15:09
I was out of town on business for most of the week… and I didn’t take any math books with me. It feels like forever since I’ve even looked at math. We’ll see what happens today. I’d like to have some fun. I don’t sleep well in hotels in general, nor in other time zones… [...]
Updated: 2012-08-18 12:25:08
Let’s pause and catch our breath with an actual example of some of the things we’ve been talking about. Specifically, we’ll consider — the special linear Lie algebra on a two-dimensional vector space. This is a nice example not only because it’s nicely representative of some general phenomena, but also because the algebra itself is [...]
Updated: 2012-08-18 12:22:18
Sorry for the delay; I’ve had a couple busy days. Here’s Thursday’s promised installment. An automorphism of a Lie algebra is, as usual, an invertible homomorphism from onto itself, and the collection of all such automorphisms forms a group . One obviously useful class of examples arises when we’re considering a linear Lie algebra . [...]
Updated: 2012-08-14 00:19:09
The following books have been added to the bibliography. Atkinson, A.C. Plots, Transformations and Regression. Oxford Science Publications, reprinted 1988. ISBN 0 19 853359 4. [regression; 13 Aug 2012] This is devoted to detecting outliers (i.e. using single deletion statistics) and to transformations of the variables. It looks like an excellent supplement to Draper and [...]
Updated: 2012-08-11 16:46:40
It’s been about as slow a week as I’ve ever had… I couldn’t even justify a headlines ticker-tape today. My alter ego the kid has been looking at surfaces again… my alter ego the grad student has been looking at so-called “arithmetic functions”. My main personality is thinking I should elaborate on the latest regression [...]
