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Robin Chapman
Robin Chapman
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Let $G$ be a finite group acting on an associative $k$-algebra with unity ($k$ algebraically closed of characteristic zero). The action is called ergodic if $ A^G = \{a \in A | g \cdot a = a, \forall g \in G \} = k$$ A^G = \{ a \in A | g \cdot a = a, \forall g \in G \} = k$.

Anyone know an example of a non-semisimple finite dimensional algebra with an ergodic action of a finite group?

Let $G$ be a finite group acting on an associative $k$-algebra with unity ($k$ algebraically closed of characteristic zero). The action is called ergodic if $ A^G = \{a \in A | g \cdot a = a, \forall g \in G \} = k$.

Anyone know an example of a non-semisimple finite dimensional algebra with an ergodic action of a finite group?

Let $G$ be a finite group acting on an associative $k$-algebra with unity ($k$ algebraically closed of characteristic zero). The action is called ergodic if $ A^G = \{ a \in A | g \cdot a = a, \forall g \in G \} = k$.

Anyone know an example of a non-semisimple finite dimensional algebra with an ergodic action of a finite group?

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César Galindo
César Galindo
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A question on group action on algebras

Let $G$ be a finite group acting on an associative $k$-algebra with unity ($k$ algebraically closed of characteristic zero). The action is called ergodic if $ A^G = \{a \in A | g \cdot a = a, \forall g \in G \} = k$.

Anyone know an example of a non-semisimple finite dimensional algebra with an ergodic action of a finite group?