Notes for AKT-090924-2/0:15:13: Difference between revisions
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Example: Space of all polynomial with two variables with rational coefficient, with co-multiplication <math>\Delta: \mathbb{Q}[x,y] \rightarrow \mathbb{Q}[x,y] \otimes \mathbb{Q}[x,y]</math> be <math>\Delta(f(x,y)) = f(x_1+x_2, y_1+y_2)</math> where <math>x_1</math> corresponds to an <math>x</math> (or <math>y</math>) before the tensor sign and <math>x_2</math> being after the tensor sign, similarly for <math>y</math>. |
Example: Space of all polynomial with two variables with rational coefficient, with co-multiplication <math>\Delta: \mathbb{Q}[x,y] \rightarrow \mathbb{Q}[x,y] \otimes \mathbb{Q}[x,y]</math> be <math>\Delta(f(x,y)) = f(x_1+x_2, y_1+y_2)</math> where <math>x_1</math> corresponds to an <math>x</math> (or <math>y</math>) before the tensor sign and <math>x_2</math> being after the tensor sign, similarly for <math>y</math>. |
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Co-unit being the map sending each polynomial to its constant term. |
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Check that this is a co-algebra (together with the usual polynomial multiplication, this space is a bi-algebra) |
Check that this is a co-algebra (together with the usual polynomial multiplication, this space is a bi-algebra) |
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Latest revision as of 02:51, 26 September 2009
Example: Space of all polynomial with two variables with rational coefficient, with co-multiplication be where corresponds to an (or ) before the tensor sign and being after the tensor sign, similarly for . Co-unit being the map sending each polynomial to its constant term. Check that this is a co-algebra (together with the usual polynomial multiplication, this space is a bi-algebra)
![{\displaystyle \Delta :\mathbb {Q} [x,y]\rightarrow \mathbb {Q} [x,y]\otimes \mathbb {Q} [x,y]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a4113d7a7bf008be4d6da80d2a4fd931baf9aba)
