Tensors, multivectors, wedge products, multilinear maps, exterior (Grassmann) algebras.

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6
votes
0answers
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Augmentation ideal is finitely generated if and only if $A$ is finitely generated as a $k$-algebra?

Let $A \subset k[x_1, \dots, x_n]$ be a subalgebra, which is also a graded subspace $A = \oplus_{i \ge 0} A_i$. One can write $A = A_0 \oplus A_{> 0}$ where we have $A_0 = k^0[x_1, \dots, x_n] = k$ ...
5
votes
1answer
118 views

Norm of $n$-linear symmetric forms

Let $B$ be a symmetric bilinear form over a Euclidean space $E$. Say that $|B(v,v)|\le c\|v\|^2$ for every $v\in E$, for some $c\ge0$. Then $$4B(v,w)=B(v+w)+B(v-w)$$ yields $2|B(v,w)|\le ...