You are Here: Home

# Mappings

Announcements Posted on
Talking about ISA/EMPA specifics is against our guidelines - read more here 28-04-2016
1. If V is a 3-dimensional Lie algebra with basis vectors E,F,G with Lie bracket relations [E,F]=G, [E,G]=0, [F,G]=0 and V' is the Lie algebra consisting of all 3x3 strictly upper triangular matrices with complex entries then would you say the following 2 mappings (isomorphisms) are different? I had to give an example of 2 different isomorphisms between these vector spaces.

given by

and given by

2. Maybe this post is a little late given that the thread is a week old now, but recall that Lie algebra isomorphisms are also linear transformations, so are determined by their values on the basis elements E,F and G. So it seems your two maps are the same. However, the map you've given is an isomorphism and from this, it doesn't look too difficult to find a second?

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 16, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How to predict exam questions

No crystal ball required

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams