# Messages List

1355

### Re: R-Algebra of dimension 4 and 8

Nice! What I like about the Mironovs' approach is that their framework remains on associative algebra, yet they are able to model fields mediated by spin-1 and
jens_koeplinger

Nov 16, 2014

#1355
1354

### Re: R-Algebra of dimension 4 and 8

Hi everyone, Following Jens's idea I studied Octons and Sedeons algebras and found a matrix representation of the octons (not included in the articles I read),
mediatmath

Nov 14, 2014

#1354
1353

### Re: Correction - Re: Commutativity Invariance

I just noticed I never posted the correction, and a correction is needed indeed. We start with an algebra that is built over a real vector space in n
jens_koeplinger

Oct 26, 2014

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1352

### Correction - Re: Commutativity Invariance

... This is nonsense, I have to think it through.
jens_koeplinger

Oct 15, 2014

#1352
1351

### Re: Commutativity Invariance

I'm not sure ... In my last post I acidentally introduced the property of orthogonal transformations U to be diagonalizable, however, without actually using
jens_koeplinger

Oct 15, 2014

#1351
1350

### Re: Commutativity Invariance

Hi Jens This is the multiplication table for generalized quaternion R^4(I,J,A,K) *.|1........x......y.......z --+--------------------------
armahedi

Oct 14, 2014

#1350
1349

### Re: Commutativity Invariance

Hi Jens Thank you for your notational innovation of * to shorten formulas. Glad that you enjoy my inovation of multiplication matrix :) You're right, it can
armahedi

Oct 14, 2014

#1349
1348

### Re: Commutativity Invariance

Hi - sorry I just threw out that one comment about linear transformations yesterday, I should have spent a bit more time and brush up on my linear algebra
jens_koeplinger

Oct 13, 2014

#1348
1347

### Re: Commutativity Invariance

Yes this is curious. [Sorry for by belated response, this year I picked up playing chess again after 25 years and am enjoying it too much] In the case of
jens_koeplinger

Oct 12, 2014

#1347
1346

### Re: Commutativity Invariance

Hi Jens, the fact that linear algebra isomorphism can not be represented by linear transformation is new to me. I will study your attached paper more closely.
armahedi

Oct 10, 2014

#1346
1345

### Re: Commutativity Invariance

Hi Philippe, Thank you for showing my foolishness believing the trace as the signature. It means that I am confused about scalar trace and "vectorial"
armahedi

Oct 10, 2014

#1345
1344

### Re: Commutativity Invariance

Hi Jens I'd also like to point out that you can have two algebras with identical properties and still will not be able to transform them into one another
mediatmath

Oct 10, 2014

#1344
1343

### Re: Commutativity Invariance

Hi - this is interesting. Next to algebraic properties, I'd also like to point out that you can have two algebras with identical properties and still will not
jens_koeplinger

Oct 10, 2014

#1343
1342

### Re: Commutativity Invariance

Hi Arma, I don't get where you are heading to : of course an isomorphism between algebra preserves commutativity, associativity, and so on ... this is the
mediatmath

Oct 10, 2014

#1342
1341

### Commutativity Invariance

Hi all In this letter I will try to prove that isomorphic generalized quaternions are having the same commutativity. Theorem (commutation Invariance)
armahedi

Oct 10, 2014

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