Timeline for Using computer algebra to check if a family of algebras are pair-wise non-isomorphic
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 15, 2021 at 15:09 | vote | accept | Sergey Guminov | ||
| Jan 15, 2021 at 14:09 | comment | added | YCor | OK, I wrote it as an answer then. | |
| Jan 15, 2021 at 14:08 | answer | added | YCor | timeline score: 1 | |
| Jan 15, 2021 at 14:04 | comment | added | Sergey Guminov | @YCor Thank you! That was exactly what I was looking for. By this criterion, this is a trivial deformation after all. | |
| Jan 13, 2021 at 19:04 | comment | added | YCor | There's a practical computer-algebra way to determine whether (a) they're all isomorphic up to finitely many exceptions or (b) there "(bounded finite)-to-one" non-isomorphic, i.e., there exists $n$ such that for each $t$ the set of $s$ such that $A_s\simeq A_t$ has cardinal $\le n$. See mathoverflow.net/questions/378149/… | |
| Jan 13, 2021 at 17:51 | comment | added | Benjamin Steinberg | In the semigroup case you would look at what the isomorphism does to multiples of matrix units. But in your setting this may not work because there are no units in the matrix $X_t$ which we usually want in the semigroup setting | |
| Jan 13, 2021 at 17:48 | comment | added | Benjamin Steinberg | The obvious guess is the algebras are isomorphic iff there are invertible 2x2 matrices P,Q over R and an automorphism $\phi$ of $R$ with $P\phi(X_t)Q=X_m$. At least your is what happens in the semigroup setting | |
| Jan 13, 2021 at 17:45 | comment | added | Benjamin Steinberg | You are looking at an example of a Rees matrix ring sciencedirect.com/science/article/pii/002186938390193X over the contracted monoid algebra of the four element monoid 1,x,y,0 with all products not involving 1 equal to zero. For Rees matrix semigroups there are characterizations of isomorphism but I am not so sure in this context | |
| Jan 13, 2021 at 17:03 | answer | added | tim | timeline score: 2 | |
| Jan 13, 2021 at 14:16 | history | asked | Sergey Guminov | CC BY-SA 4.0 |