Where can I find coderivations?
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I have recently stumbled upon the notion of a coderivation. I had been working with twisted coderivations for a while, without realizing they there was a name for them (and probably some nice treatment in the literature). For me it was just an extra condition.
Without further ado, a twisted coderivation, say a $a$-coderivation (for some element $a$ in a algebra Hopf algebra $R$) is a map $d colon R rightarrow R$ such that
$$Delta d(r) = d(r_1) otimes r_2 + a r_1 otimes d(r_2)$$
for any $r in R$ in Sweedler notation or simply, $Delta d = (d otimes 1 + a otimes d) Delta$.
I want to find where the concept of coderivation (twisted and/or not) was first defined. Any other good references, where there is a treatment of the topic, are greatly appreciated. I have looked myself some books on Hopf Algebras like Sweedler, Montgomery and Radford. Only Radford had the definition of coderivation and some results (exercises actually) about it, but it is only a partial answer.
reference-request hopf-algebras coalgebras
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
$endgroup$
add a comment |
$begingroup$
I have recently stumbled upon the notion of a coderivation. I had been working with twisted coderivations for a while, without realizing they there was a name for them (and probably some nice treatment in the literature). For me it was just an extra condition.
Without further ado, a twisted coderivation, say a $a$-coderivation (for some element $a$ in a algebra Hopf algebra $R$) is a map $d colon R rightarrow R$ such that
$$Delta d(r) = d(r_1) otimes r_2 + a r_1 otimes d(r_2)$$
for any $r in R$ in Sweedler notation or simply, $Delta d = (d otimes 1 + a otimes d) Delta$.
I want to find where the concept of coderivation (twisted and/or not) was first defined. Any other good references, where there is a treatment of the topic, are greatly appreciated. I have looked myself some books on Hopf Algebras like Sweedler, Montgomery and Radford. Only Radford had the definition of coderivation and some results (exercises actually) about it, but it is only a partial answer.
reference-request hopf-algebras coalgebras
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
$endgroup$
add a comment |
$begingroup$
I have recently stumbled upon the notion of a coderivation. I had been working with twisted coderivations for a while, without realizing they there was a name for them (and probably some nice treatment in the literature). For me it was just an extra condition.
Without further ado, a twisted coderivation, say a $a$-coderivation (for some element $a$ in a algebra Hopf algebra $R$) is a map $d colon R rightarrow R$ such that
$$Delta d(r) = d(r_1) otimes r_2 + a r_1 otimes d(r_2)$$
for any $r in R$ in Sweedler notation or simply, $Delta d = (d otimes 1 + a otimes d) Delta$.
I want to find where the concept of coderivation (twisted and/or not) was first defined. Any other good references, where there is a treatment of the topic, are greatly appreciated. I have looked myself some books on Hopf Algebras like Sweedler, Montgomery and Radford. Only Radford had the definition of coderivation and some results (exercises actually) about it, but it is only a partial answer.
reference-request hopf-algebras coalgebras
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
$endgroup$
I have recently stumbled upon the notion of a coderivation. I had been working with twisted coderivations for a while, without realizing they there was a name for them (and probably some nice treatment in the literature). For me it was just an extra condition.
Without further ado, a twisted coderivation, say a $a$-coderivation (for some element $a$ in a algebra Hopf algebra $R$) is a map $d colon R rightarrow R$ such that
$$Delta d(r) = d(r_1) otimes r_2 + a r_1 otimes d(r_2)$$
for any $r in R$ in Sweedler notation or simply, $Delta d = (d otimes 1 + a otimes d) Delta$.
I want to find where the concept of coderivation (twisted and/or not) was first defined. Any other good references, where there is a treatment of the topic, are greatly appreciated. I have looked myself some books on Hopf Algebras like Sweedler, Montgomery and Radford. Only Radford had the definition of coderivation and some results (exercises actually) about it, but it is only a partial answer.
reference-request hopf-algebras coalgebras
reference-request hopf-algebras coalgebras
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
edited Aug 20 '16 at 12:49
Najib Idrissi
41.9k473143
41.9k473143
asked Aug 20 '16 at 12:42
solidsolid
917
asked Aug 20 '16 at 12:42
solidsolid
917
asked Aug 20 '16 at 12:42
solidsolid
917
917
add a comment |
add a comment |
1 Answer
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The concept of coderivation was first defined by Yukio Doi in order to study ''Homological coalgebra''. If you want to lear more details about coderivation, you can see this Ref
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1239888030
answered Jan 11 at 3:14
DaisyDaisy
472413
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add a comment |
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1 Answer
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1 Answer
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active
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$begingroup$
The concept of coderivation was first defined by Yukio Doi in order to study ''Homological coalgebra''. If you want to lear more details about coderivation, you can see this Ref
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1239888030
answered Jan 11 at 3:14
DaisyDaisy
472413
$endgroup$
add a comment |
$begingroup$
The concept of coderivation was first defined by Yukio Doi in order to study ''Homological coalgebra''. If you want to lear more details about coderivation, you can see this Ref
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1239888030
answered Jan 11 at 3:14
DaisyDaisy
472413
$endgroup$
add a comment |
$begingroup$
The concept of coderivation was first defined by Yukio Doi in order to study ''Homological coalgebra''. If you want to lear more details about coderivation, you can see this Ref
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1239888030
answered Jan 11 at 3:14
DaisyDaisy
472413
$endgroup$
The concept of coderivation was first defined by Yukio Doi in order to study ''Homological coalgebra''. If you want to lear more details about coderivation, you can see this Ref
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1239888030
answered Jan 11 at 3:14
DaisyDaisy
472413
answered Jan 11 at 3:14
DaisyDaisy
472413
answered Jan 11 at 3:14
DaisyDaisy
472413
answered Jan 11 at 3:14
DaisyDaisy
472413
472413
add a comment |
add a comment |
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