Mixing
Tensor of vector space [closed]
0
$begingroup$
Suppose that $V =text{span}(1,x)$ is a vector space over $frac{mathbb{Z}}{2mathbb{Z}} $ and let
$delta : V rightarrow Votimes V$
Such that $delta (1) = 1otimes x + xotimes 1$ and $delta (x) = x otimes x$.
What is the kernel of $delta$?
linear-algebra abstract-algebra tensor-products
asked Jan 8 at 0:28
fatemefateme
294
$endgroup$
closed as off-topic by Saad, jgon, zipirovich, Shailesh, mrtaurho Jan 8 at 6:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, jgon, zipirovich, Shailesh, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
0
$begingroup$
Suppose that $V =text{span}(1,x)$ is a vector space over $frac{mathbb{Z}}{2mathbb{Z}} $ and let
$delta : V rightarrow Votimes V$
Such that $delta (1) = 1otimes x + xotimes 1$ and $delta (x) = x otimes x$.
What is the kernel of $delta$?
linear-algebra abstract-algebra tensor-products
asked Jan 8 at 0:28
fatemefateme
294
$endgroup$
closed as off-topic by Saad, jgon, zipirovich, Shailesh, mrtaurho Jan 8 at 6:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, jgon, zipirovich, Shailesh, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
1
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48
add a comment |
0
0
0
1
$begingroup$
Suppose that $V =text{span}(1,x)$ is a vector space over $frac{mathbb{Z}}{2mathbb{Z}} $ and let
$delta : V rightarrow Votimes V$
Such that $delta (1) = 1otimes x + xotimes 1$ and $delta (x) = x otimes x$.
What is the kernel of $delta$?
linear-algebra abstract-algebra tensor-products
asked Jan 8 at 0:28
fatemefateme
294
$endgroup$
Suppose that $V =text{span}(1,x)$ is a vector space over $frac{mathbb{Z}}{2mathbb{Z}} $ and let
$delta : V rightarrow Votimes V$
Such that $delta (1) = 1otimes x + xotimes 1$ and $delta (x) = x otimes x$.
What is the kernel of $delta$?
linear-algebra abstract-algebra tensor-products
linear-algebra abstract-algebra tensor-products
asked Jan 8 at 0:28
fatemefateme
294
asked Jan 8 at 0:28
fatemefateme
294
edited Jan 8 at 17:15
fateme
asked Jan 8 at 0:28
fatemefateme
294
asked Jan 8 at 0:28
fatemefateme
294
asked Jan 8 at 0:28
fatemefateme
294
294
closed as off-topic by Saad, jgon, zipirovich, Shailesh, mrtaurho Jan 8 at 6:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, jgon, zipirovich, Shailesh, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, jgon, zipirovich, Shailesh, mrtaurho Jan 8 at 6:02
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, jgon, zipirovich, Shailesh, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
1
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
1
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48
add a comment |
1
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
1
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48
1
1
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
1
1
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48
add a comment |
1 Answer
1
active
oldest
votes
1
$begingroup$
Hint: To show that $delta$ has a trivial kernel, it suffices to show that $delta(1)$ and $delta(x)$ are linearly independent.
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
$endgroup$
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
$begingroup$
Hint: To show that $delta$ has a trivial kernel, it suffices to show that $delta(1)$ and $delta(x)$ are linearly independent.
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
$endgroup$
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
add a comment |
1
$begingroup$
Hint: To show that $delta$ has a trivial kernel, it suffices to show that $delta(1)$ and $delta(x)$ are linearly independent.
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
$endgroup$
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
add a comment |
1
1
1
$begingroup$
Hint: To show that $delta$ has a trivial kernel, it suffices to show that $delta(1)$ and $delta(x)$ are linearly independent.
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
$endgroup$
Hint: To show that $delta$ has a trivial kernel, it suffices to show that $delta(1)$ and $delta(x)$ are linearly independent.
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
answered Jan 8 at 0:35
OmnomnomnomOmnomnomnom
128k790179
128k790179
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
add a comment |
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
$begingroup$
Almost. This isn't true when (say) $x=0$.
$endgroup$
– darij grinberg
Jan 8 at 0:59
1
1
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Darij In this context, I think $x$ is meant to be taken as a function (or formal symbol) rather than as a particular value
$endgroup$
– Omnomnomnom
Jan 8 at 1:42
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
$begingroup$
@Omnomnomnom exactly right. this question related to khovanov homology and x is a formal symbol.
$endgroup$
– hussein
Jan 8 at 21:39
add a comment |
1
$begingroup$
What are your thoughts on the problem? What have you tried?
$endgroup$
– Omnomnomnom
Jan 8 at 0:33
1
$begingroup$
Do you know the dimension of $Votimes V$? Can you set up a basis?
$endgroup$
– Berci
Jan 8 at 0:36
$begingroup$
basis of $V bigotimes V$ are $1otimes 1 , 1otimes x, x otimes 1$, and$ x otimes x$ /then kernel of $delta$ is zero.
$endgroup$
– hussein
Jan 8 at 14:48