Timeline for Lie algebras : Deformations and Rigidity
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2021 at 20:26 | vote | accept | Hamidreza Safari | ||
| Mar 13, 2018 at 4:58 | comment | added | Theo Johnson-Freyd | Specifically, my guess is that for the purpose of the question, the Witt algebra could be any semisimple Lie algebra $\mathfrak{g}$, and OP's algebra is $\mathfrak{g} \ltimes \mathfrak{g}_{adj}$, where by $\mathfrak{g}_{adj}$ I mean the adjoint $\mathfrak{g}$-module (thought of as an abelian Lie algebra). | |
| Mar 13, 2018 at 4:56 | comment | added | Theo Johnson-Freyd | @YCor OP is a physicist, I believe. My guess is that he will be happy with any reasonable choices for topological issues. Analytic questions about Virasoro are myriad, exciting, important, and mostly ignored by physicist practitioners. | |
| Mar 12, 2018 at 11:43 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Mar 12, 2018 at 11:01 | history | edited | Hamidreza Safari | CC BY-SA 3.0 |
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| Mar 12, 2018 at 10:20 | answer | added | Nicola Ciccoli | timeline score: 4 | |
| Mar 12, 2018 at 9:08 | history | edited | Hamidreza Safari | CC BY-SA 3.0 |
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| Mar 12, 2018 at 8:22 | comment | added | YCor | I pointed the issue of infinite dimension. Intuition and analogies are one thing, but at some point you need to define objects (deformations, (co)homology...) and this will be sensitive to the setting. At this point all is very vague: I have no idea if you have in mind abstract Lie algebras over arbitrary fields, continuous brackets on Banach spaces, anything in relation with the tag "algebraic geometry"... | |
| Mar 12, 2018 at 7:53 | comment | added | Hamidreza Safari | As I understand deformation of Lie algebra is related to its second adjoint cohomology, so if this cohomology is nontrivial Lie algebra would admit a deformation. Lie algebras I am working on are defined on fields with characteristic zero (for example real numbers). | |
| Mar 12, 2018 at 7:41 | comment | added | YCor | Could you be a little more specific about the setting, so as to clarify the meaning of "deformation"? Lie algebras over which field? deformation in a topological sense? (I imagined so but you also tagged "algebraic-geometry", so...) and topological deformation is sensitive to choices of topology in infinite dimension. | |
| Mar 12, 2018 at 7:38 | history | asked | Hamidreza Safari | CC BY-SA 3.0 |