Timeline for "Natural" pairings between exterior powers of a vector space and its dual
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2021 at 13:53 | history | edited | LSpice | CC BY-SA 4.0 |
Link to @TorstenEkedahl's comment while this is on the front page
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| Dec 3, 2021 at 18:55 | comment | added | Alexey Muranov | Sorry, but could someone please clarify for non-specialists which pairing is "the most natural" one according to Torsten's answer? | |
| Jun 17, 2011 at 14:16 | comment | added | Theo Johnson-Freyd | @unknowngoogle: yes, that's a typo. @Scott: If you only care about normal vector spaces, then you certainly can do this. If you care about constructions that generalize to supervector spaces, or to any other not-very-concrete category, then you cannot. @Torsten: Ok, so I must have made an error. I've thought a lot more about the details in the symmetric algebra case, where I am sure that the Hopf map is not an iso in general. | |
| Jun 17, 2011 at 12:53 | comment | added | Qfwfq | If you want to obtain the exterior algebra, I think the ideal by wich to quotient should be $\langle v_1\otimes v_2 + v_2\otimes v_1 \rangle$. | |
| Jun 17, 2011 at 4:44 | comment | added | Torsten Ekedahl | With the correction made by Scott it always is an isomorphism, use that the exterior algebra takes directs sums to tensor products to reduce to dimension 1 where it is obvious. | |
| Jun 17, 2011 at 3:08 | comment | added | S. Carnahan♦ | I think your definition of exterior algebra needs to be changed when 2 is not invertible. The ideal should be generated by elements of the form $x \otimes x$. | |
| Jun 17, 2011 at 2:37 | history | answered | Theo Johnson-Freyd | CC BY-SA 3.0 |