Timeline for Does $\mathcal{A}\otimes\mathbb{C}(t)\cong\mathcal{D}\otimes\mathbb{C}(t)$ imply an isomorphism of Lie algebras?

8 events

when toggle format	what		by	license	comment
Jul 24, 2020 at 6:58	vote	accept	solver6
Jul 23, 2020 at 16:49	comment	added	Joshua Mundinger		@მამუკაჯიბლაძე the $t$-adic topology on $K((t))$ doesn't play well with embedding into $\mathbb C$.
Jul 23, 2020 at 10:38	comment	added	მამუკა ჯიბლაძე		I wonder why a similar argument would not work with $\mathbb C((t))$...
Jul 23, 2020 at 10:09	comment	added	solver6		So you proved the more general fact that if $\mathcal{A}\otimes_{\mathbb{C}}\mathbb{C}(t)$ is isomorphic as $\mathbb{C}(t)$-Lie algebra to $\mathcal{B}\otimes_{\mathbb{C}}\mathbb{C}(t)$ and $\dim_{\mathbb{C}}\mathcal{A}=\dim_{\mathbb{C}}\mathcal{B}$-countable then $\mathcal{A}$ is isomorphic to $\mathcal{B}$ as $\mathbb{C}$-Lie algebra. Is there any known reference to this fact existed in literature?
Jul 23, 2020 at 10:00	history	edited	Neil Strickland	CC BY-SA 4.0	Clarified the meaning of "structure constants"
Jul 23, 2020 at 10:00	comment	added	solver6		If by structure constants you mean coordinates of commutators of elements from a countable basis then it looks as a correct proof for me. I need to think more about it to mark as accepted
Jul 23, 2020 at 9:52	comment	added	solver6		Thank you. I don't have enough knowledge about structure constants, so right now I cannot check your proof completely. From the answer we have that 1), 2) are true, but what about 3)?
Jul 23, 2020 at 9:04	history	answered	Neil Strickland	CC BY-SA 4.0