Timeline for Iterated Reduced Tensor Power of Graded Vector spaces
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2013 at 5:17 | comment | added | Peter Michor | You decided to ignore the grade $k$ which exactly encodes your feeling that "all the tensor powers are already there". But in $\overline{T}\overline{T}(V)$ they are there multiple times; you then have 3 degrees and cannot reduce them to 2 correctly. | |
| Jul 22, 2013 at 16:16 | comment | added | Nevermind | But as I said, the graded tensor power makes $\overline{T}(V)$ into a $\mathbb{Z}$-graded vector space by $\overline{T}(V)_j:=\oplus_{k}\oplus_{p_1,\ldots,p_k=j}V_{p_1}\otimes \cdots\otimes V_{p_k}$, where each $p_h\geq 1$. | |
| Jul 22, 2013 at 16:06 | comment | added | Nevermind | And by the way: $\overline{T}$ is in addition a functor into the category of locally nilpotent graded coassociative coalgebras and there it is right adoint to the forgetful functor | |
| Jul 22, 2013 at 15:52 | history | answered | Peter Michor | CC BY-SA 3.0 |