bialgebra (Q6196): Difference between revisions

Latest revision as of 20:31, 31 March 2023

vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way

Language	Label	Description	Also known as
English	bialgebra	vector space which is both a unital associative algebra and a counital coassociative coalgebra in a compatible way

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{\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 @@
+quasi-bialgebra
@@ Property / subclass of: quasi-bialgebra / rank @@
+Normal rank
@@ Property / defining formula @@
+ ${\begin{aligned}\Delta \circ \nabla &=\nabla \otimes \nabla \circ (\operatorname {id} \otimes \sigma \otimes \operatorname {id} )\circ \Delta \otimes \Delta \\\epsilon \otimes \epsilon &=\epsilon \circ \nabla \\\eta \otimes \eta &=\Delta \circ \eta \\\epsilon \circ \eta &=\operatorname {id} \end{aligned}}$ 
\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}
+Normal rank