Timeline for Why should we study derivations of algebras?
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18 events
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| Jul 14 at 21:28 | answer | added | Skip | timeline score: 3 | |
| Aug 22, 2020 at 13:22 | comment | added | LSpice | @rschwieb's reference: Shanks and Pursell - The Lie algebra of a smooth manifold. | |
| Jul 12, 2018 at 19:59 | comment | added | Nicola Ciccoli | Yes, that's it. | |
| Jul 12, 2018 at 17:14 | comment | added | rschwieb | @NicolaCiccoli Is this the original paper for said theorem? jstor.org/stable/2031961?seq=1#page_scan_tab_contents | |
| Jul 12, 2018 at 8:21 | answer | added | Matthias Wendt | timeline score: 9 | |
| Jul 12, 2018 at 7:42 | answer | added | user21230 | timeline score: 4 | |
| S Jul 12, 2018 at 6:54 | history | suggested | David G. Stork | CC BY-SA 4.0 |
Clarified and improved grammar
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| Jul 12, 2018 at 3:08 | comment | added | spin | I am not sure what kind of answer you are looking for, but here is one basic remark. For an algebra, the composition of two derivations is not necessarily a derivation, but the set of derivations is closed under the commutator bracket and they form a Lie algebra. Derivations of Lie algebras are a fundamental concept in the study of Lie algebras and their representations. In some sense derivations of Lie algebras are analogous to automorphisms of groups (Lie algebras act on Lie algebras by derivations, while groups act on groups by automorphisms). | |
| Jul 11, 2018 at 23:27 | review | Suggested edits | |||
| S Jul 12, 2018 at 6:54 | |||||
| Jul 11, 2018 at 23:04 | history | reopened |
Nik Weaver Benjamin Steinberg Guntram Stefan Kohl♦ Yemon Choi |
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| Jul 11, 2018 at 19:43 | review | Reopen votes | |||
| Jul 11, 2018 at 23:04 | |||||
| Jul 11, 2018 at 18:39 | history | closed |
Loïc Teyssier abx YCor Piotr Hajlasz Qiaochu Yuan |
Not suitable for this site | |
| Jul 11, 2018 at 17:03 | comment | added | Nicola Ciccoli | Just as a side comment to the last question: I was surprised when I learned only much later than I would have liked to, that the algebra of all continuous functions (say on a manifold) has only the zero derivation, in striking contrast to its dense subalgebra of smooth functions. As for "a specific thing about importance" I suggest you to have a look at "Pursell-Shanks theorem". | |
| Jul 11, 2018 at 16:22 | answer | added | Nik Weaver | timeline score: 18 | |
| Jul 11, 2018 at 14:48 | review | Close votes | |||
| Jul 11, 2018 at 18:43 | |||||
| Jul 11, 2018 at 14:31 | comment | added | Yemon Choi | I think this is a perfectly reasonable question, although it should probably be clarified if the OP is mainly interested in the functional-analytic versions or not. Certainly I have refereed far too many papers proving things (of varying depth and worth) about derivations on Banach algebras, which don't seem to pause to address the questions raised by the OP | |
| Jul 11, 2018 at 14:08 | review | First posts | |||
| Jul 11, 2018 at 15:18 | |||||
| Jul 11, 2018 at 14:05 | history | asked | Ilma Azzahra | CC BY-SA 4.0 |