## 290 Reputation

9 years, 190 days

## Not working !!!...

The following code was sent by Ian Anderson himself and is not working as suggested:

Optimal1.mw

## Stucked again......!!!!...

What should I do after this?

What is this initilization ?

Please illustrate in Maple sheet attached with

## That's good........but !...

That really calculate position of stationary points, but how do one know whether this stationary point is for Maxima or Minima ??

That is nice and quick reponse.

But how do I subtitute 8 triplet into expression that is what I really asked for?

## dsubs as alternative for subs...

Everything is explained by ecterrab except replacement of derivative u[t] in DetSys, that can be done by command "dsubs". This command do same job as "subs" do, but using "dsubs" one can replace derivative which one can not perform using "subs" command.

Regards

## Yes...

I have tried that command but I think I am using it in wrong way.

## See this decompositon...

Please see following decompositon you requested

 >
 (1)
 >
 (2)
 >
 >
 (3)
 >
 (4)
 Alg1   >
 >
 (5)

 Alg1 >
 (6)
 Ex2 >

## Book...

Thank you so much.

Pavel Winternitz and Peter Olver both suggested me following book on classification of Lie algebras:

L. Snobl and P. Winternitz, Classification and Identification of Lie
algebras, CRM Monograph Series, Vol 33, AMS, Providence, RI, 2014.

I believe this book could be helpful in understanding classification problems in Lie algebra, but unfortunately I can not afford this book.

## Decomposition...

Following may also be suitable

 >
 >
 >
 Euc >
 (1)
 Euc >
 (2)
 Euc >
 (3)
 L1 >
 (4)
 L1 >
 (5)
 L1 >

## Wrong Judgement...

I made early judgement as I am beginner in Lie algebra. Actually my field is Lie group analysis of partial differential equations and during literature survey I come to realise that abstract Lie algebras are better suitable for classification of Lie algebras for group invariant solutions.

I do not even know how you could make decision about decomposition from multiplication table.

Can you please explain how you read mutliplication table for L_1 ?

Or please suggest any good graduate text on Lie algebra. I have books like of Nathan Jacobson but that seems to be too advance for me.

## But I Guess.........!!!...

But I guess the decomposition must be like

L = L_1 + L_2 + L_3 + L_4

with

L_1 = { V-2-V_1, V_3, V_4} = sl(2,R),

L_2 = {{V_6, V_7, V_5} , L_3 },

L_3= {V_1+V_2},

L_3 ={{V_8}

Please correct me if I am wrong.

## Wow........!!!!...

Thank you So much.

One more thing, can you please tell how to express this abstract Lie algebra as direct sum of indecomposable Lie algebras.

and how to perform in reverse manner i.e. to convert this abstract Lie algebra to Lie algebra?

## Amazing...........

Thanks for help.

I am really grateful to you and I wish for your healthy and peaceful life.

## I failed to explain..................

I am carrying put succssive adjoints on linear combination of vectors. These adjoint actions are being carried out with the aid of Matrix called adjoint matrix. Please see following:

 >
 (1)

Step I

 >
 (1.1)
 >
 (1.2)
 >
 (1.3)

Step II

 >

The expression from previous step is used here

 (2.1)
 >
 (2.2)
 >
 (2.3)

Step III

 >
 (3.1)
 >
 (3.2)
 >
 (3.3)

Step IV

 >
 (4.1)
 >
 (4.2)
 >
 (4.3)

Can we combine above four step in single sequence ?