Timeline for Extension of automorphism of shift of finite type
Current License: CC BY-SA 4.0
14 events
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| Apr 20 at 9:56 | comment | added | Ali Ahmadi | Very interesting point, thank you so much for sharing it. | |
| Apr 20 at 8:20 | comment | added | Ville Salo | Point here being, for a full shift on prime alphabet, the dimension group representation is generated by the shift map. | |
| Apr 20 at 8:17 | comment | added | Ville Salo | I think every automorphism of 2-shift can be extended to 3-shift: kill the dimension rep by composing with shift (which extends), then inerts extend. | |
| Apr 20 at 5:33 | comment | added | Ali Ahmadi | @VilleSalo thanks for your answer. Therefore an automorphism of $\{0,1\}^{\mathbb{Z}} $ can not be extended to an automorphism of $\{0,1,2\}^{\mathbb{Z}} $. Is it true? | |
| Apr 19 at 14:43 | history | edited | YCor | CC BY-SA 4.0 |
removed confusing part of title
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| Apr 19 at 13:58 | comment | added | Ville Salo | Not in general, see mathoverflow.net/questions/452585/… (a finite shift-invariant set is a subshift of finite type) | |
| Apr 19 at 8:36 | history | edited | Ali Ahmadi | CC BY-SA 4.0 |
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| Apr 19 at 8:36 | history | edited | Ali Ahmadi | CC BY-SA 4.0 |
added 1 character in body
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| Apr 19 at 8:35 | comment | added | Ali Ahmadi | Thank you for your answer. You are right, I edited the question. | |
| Apr 19 at 8:34 | history | edited | Ali Ahmadi | CC BY-SA 4.0 |
added 26 characters in body
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| Apr 18 at 11:34 | comment | added | YCor | The two questions are not equivalent. The question asks, denoting $\mathrm{Aut}(Y,X)$ the automorphisms of $Y$ leaving $X$ invariant, whether the restriction map $\mathrm{Aut}(Y,X)\to\mathrm{Aut}(X)$ is surjective. When this is true, this map is probably not bijective, and hence it doesn't yield an embedding of $\mathrm{Aut}(X)$ into $\mathrm{Aut}(Y)$. (By the way, there are several interpretations of "is $\mathrm{Aut}(X)\subset\mathrm{Aut}(Y)$".) | |
| Apr 18 at 11:31 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| S Apr 18 at 10:41 | review | First questions | |||
| Apr 18 at 10:52 | |||||
| S Apr 18 at 10:41 | history | asked | Ali Ahmadi | CC BY-SA 4.0 |