Is Every Finite Dimensional Lie Algebra Isomorphic to a Subalgebra of GL(n)?

Kontilera
Messages
176
Reaction score
24
Is there any finite dimensional Lie algebra that is not isomorphic to any of the subalgebras contained in GL(n) ?
 
Physics news on Phys.org

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Similar threads

I The Lie algebra of ##\frak{so}(3)## without complexification
Replies
2
Views
2K
A Infinite-Dimensional Lie Algebra
Replies
4
Views
2K
A Questions about solvable Lie algebras
Replies
7
Views
2K
A About Universal enveloping algebra
Replies
4
Views
2K
I Meaning of terms in a direct sum decomposition of an algebra
Replies
8
Views
2K
I What is the definition of a Semi-simple Lie algebra?
Replies
4
Views
2K
About semidirect product of Lie algebra
Replies
19
Views
3K
A Topology on a space of Lie algebras
Replies
2
Views
3K
Insights Lie Algebras: A Walkthrough - The Representations
Replies
1
Views
2K
  • Poll Poll
A Why a Lie Group is closed in GL(n,C)?
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top