Timeline for Origin of the sign convention in the Tensor product of graded vector spaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2017 at 0:07 | vote | accept | Mark.Neuhaus | ||
| Nov 9, 2017 at 0:06 | vote | accept | Mark.Neuhaus | ||
| Nov 9, 2017 at 0:07 | |||||
| May 10, 2012 at 20:39 | comment | added | Mike Shulman | Even more geometrically, the twist isomorphism $S^n \wedge S^k \cong S^k \wedge S^n$ has degree $(-1)^{n k}$ under the identification of both sides with $S^{n+k}$. | |
| May 10, 2012 at 12:59 | answer | added | Jake | timeline score: 8 | |
| May 10, 2012 at 11:54 | answer | added | Vladimir Dotsenko | timeline score: 4 | |
| May 10, 2012 at 11:15 | comment | added | Mark Grant | This is known as the Koszul sign convention. My guess (and it is only a guess) is that it has its origins in geometry: for a wedge of differential forms we have $\eta\wedge\omega = (-1)^{\operatorname{deg}(\omega)\operatorname{deg}(\eta)}\omega\wedge\eta$, which makes the exterior derivative well-behaved and keeps track of orientations. | |
| May 10, 2012 at 10:55 | history | asked | Mark.Neuhaus | CC BY-SA 3.0 |