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Results tagged with vector-spaces
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user 140180
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A description of the kernel of projection map from the tensor algebra to the symmetric algeb...
Let $V$ be a vector space over some arbitrary field. Let $T(V)$ and $S(V)$ be the tensor and symmetric algebras over $V$. We have the projection map $T(V)\to S(V)$, given by $x_1\otimes\cdots\otimes x …
3
votes
1
answer
139
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The "semi-symmetric" algebra of a vector space
If $V$ is a vector space over a field $K$, then the symmetric algebra $S(V)$ is defined as the tensor algebra $T(V)$ factorized by the two-sided ideal generated by $x\otimes y-y\otimes x$, with $x,y\i …
2
votes
The "semi-symmetric" algebra of a vector space
I posted a short article on arxiv. In the second section I speak about the algebra S'(V). However, the main result is in the first section, and it deals with the kernel of the projection map $T(V)\to …
2
votes
A description of the kernel of projection map from the tensor algebra to the symmetric algeb...
The proof turned out to be longer than expected, so I decided to write it in a separate paper. You may find it on arxiv here:
https://arxiv.org/abs/1912.03515
The second section deals with the "semi- …