Item:Q6196: Difference between revisions
Created a new Item: bialgebra, vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way |
Created claim: defining formula (P333): \begin{aligned}\Delta\circ\nabla&=\nabla\otimes\nabla\circ(\operatorname{id}\otimes\sigma\otimes\operatorname{id})\circ\Delta\otimes\Delta\\\epsilon\otimes\epsilon&=\epsilon\circ\nabla\\\eta\otimes\eta&=\Delta\circ\eta\\\epsilon\circ\eta&=\operatorname{id} \end{aligned} |
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| Property / subclass of | |||
| Property / subclass of: algebra over a field / rank | |||
Normal rank | |||
| Property / subclass of | |||
| Property / subclass of: coalgebra / rank | |||
Normal rank | |||
| Property / subclass of | |||
| Property / subclass of: quasi-bialgebra / rank | |||
Normal rank | |||
| Property / defining formula | |||
\begin{aligned}\Delta\circ\nabla&=\nabla\otimes\nabla\circ(\operatorname{id}\otimes\sigma\otimes\operatorname{id})\circ\Delta\otimes\Delta\\\epsilon\otimes\epsilon&=\epsilon\circ\nabla\\\eta\otimes\eta&=\Delta\circ\eta\\\epsilon\circ\eta&=\operatorname{id} \end{aligned} | |||
| Property / defining formula: / rank | |||
Normal rank | |||
