Mixing
Does every subspace of the exterior algebra of dimension $>1$ contain a decomposable element?
$begingroup$
Let $V$ be a real $n$-dimensional vector space, and let $W le bigwedge^k V$ be a subspace . Suppose that $dim W ge 2$. Does $W$ contain a non-zero decomposable element?
If $dim W=1$, then clearly we can take $W=text{span} (sigma)$ for some non-decomposable $sigma in bigwedge^k V$.
linear-algebra representation-theory exterior-algebra tensor-decomposition
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
$endgroup$
add a comment |
$begingroup$
Let $V$ be a real $n$-dimensional vector space, and let $W le bigwedge^k V$ be a subspace . Suppose that $dim W ge 2$. Does $W$ contain a non-zero decomposable element?
If $dim W=1$, then clearly we can take $W=text{span} (sigma)$ for some non-decomposable $sigma in bigwedge^k V$.
linear-algebra representation-theory exterior-algebra tensor-decomposition
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
$endgroup$
add a comment |
$begingroup$
Let $V$ be a real $n$-dimensional vector space, and let $W le bigwedge^k V$ be a subspace . Suppose that $dim W ge 2$. Does $W$ contain a non-zero decomposable element?
If $dim W=1$, then clearly we can take $W=text{span} (sigma)$ for some non-decomposable $sigma in bigwedge^k V$.
linear-algebra representation-theory exterior-algebra tensor-decomposition
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
$endgroup$
Let $V$ be a real $n$-dimensional vector space, and let $W le bigwedge^k V$ be a subspace . Suppose that $dim W ge 2$. Does $W$ contain a non-zero decomposable element?
If $dim W=1$, then clearly we can take $W=text{span} (sigma)$ for some non-decomposable $sigma in bigwedge^k V$.
linear-algebra representation-theory exterior-algebra tensor-decomposition
linear-algebra representation-theory exterior-algebra tensor-decomposition
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
edited Jan 3 at 8:52
Asaf Shachar
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
asked Jan 2 at 13:14
Asaf ShacharAsaf Shachar
5,2473941
5,2473941
add a comment |
add a comment |
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