Symmetric algebra notation
$begingroup$
For a vector space $V$ we have its tensor algebra $TV = bigoplus _{k=0}^infty otimes ^k V$, its exterior algebra $Lambda V = bigoplus _{k=0}^infty Lambda ^k V$, and its symmetric algebra $S V = bigoplus _{k=0}^infty S ^k V$. For the first two we have a notation for their product $otimes$ and $land$. Is there a common notation for the product in $SV$? I have seen $otimes _S$, but this seems fairly unnatural, since it suggests some link between $TV$ and $SV$ that is not shared with $Lambda V$.
notation tensors
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
$endgroup$
add a comment |
$begingroup$
For a vector space $V$ we have its tensor algebra $TV = bigoplus _{k=0}^infty otimes ^k V$, its exterior algebra $Lambda V = bigoplus _{k=0}^infty Lambda ^k V$, and its symmetric algebra $S V = bigoplus _{k=0}^infty S ^k V$. For the first two we have a notation for their product $otimes$ and $land$. Is there a common notation for the product in $SV$? I have seen $otimes _S$, but this seems fairly unnatural, since it suggests some link between $TV$ and $SV$ that is not shared with $Lambda V$.
notation tensors
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
$endgroup$
add a comment |
$begingroup$
For a vector space $V$ we have its tensor algebra $TV = bigoplus _{k=0}^infty otimes ^k V$, its exterior algebra $Lambda V = bigoplus _{k=0}^infty Lambda ^k V$, and its symmetric algebra $S V = bigoplus _{k=0}^infty S ^k V$. For the first two we have a notation for their product $otimes$ and $land$. Is there a common notation for the product in $SV$? I have seen $otimes _S$, but this seems fairly unnatural, since it suggests some link between $TV$ and $SV$ that is not shared with $Lambda V$.
notation tensors
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
$endgroup$
For a vector space $V$ we have its tensor algebra $TV = bigoplus _{k=0}^infty otimes ^k V$, its exterior algebra $Lambda V = bigoplus _{k=0}^infty Lambda ^k V$, and its symmetric algebra $S V = bigoplus _{k=0}^infty S ^k V$. For the first two we have a notation for their product $otimes$ and $land$. Is there a common notation for the product in $SV$? I have seen $otimes _S$, but this seems fairly unnatural, since it suggests some link between $TV$ and $SV$ that is not shared with $Lambda V$.
notation tensors
notation tensors
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
asked Nov 29 '18 at 14:26
Joshua TilleyJoshua Tilley
546313
546313
add a comment |
add a comment |
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