Skip to main content
MathOverflow

Return to Question

edited body
Source Link
Jianrong Li
Jianrong Li
  • 6.2k
  • 2
  • 21
  • 34

In the paper, page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ h_{(1)}.v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H. $$$$ h_{(1)} v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H. $$ On the other hand, in the article, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ \delta(h.v) = h_{(1)} v_{(-1)} S(h_{(3)}) \otimes h_{(2)}.v_{(0)}, v \in V, h \in H. $$ Are the two conditions equivalent? Thank you very much.

In the paper, page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ h_{(1)}.v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H. $$ On the other hand, in the article, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ \delta(h.v) = h_{(1)} v_{(-1)} S(h_{(3)}) \otimes h_{(2)}.v_{(0)}, v \in V, h \in H. $$ Are the two conditions equivalent? Thank you very much.

In the paper, page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ h_{(1)} v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H. $$ On the other hand, in the article, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ \delta(h.v) = h_{(1)} v_{(-1)} S(h_{(3)}) \otimes h_{(2)}.v_{(0)}, v \in V, h \in H. $$ Are the two conditions equivalent? Thank you very much.

Source Link
Jianrong Li
Jianrong Li
  • 6.2k
  • 2
  • 21
  • 34

Compatibility conditions for Yetter-Drinfeld modules

In the paper, page 28, Definition 4.2.1, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ h_{(1)}.v_{(-1)} \otimes h_{(2)}.v_{(0)} = (h_{(1)}.v)_{(-1)}h_{(2)} \otimes (h_{(1)}.v)_{(0)}, v \in V, h \in H. $$ On the other hand, in the article, the compatibility condition for a Yetter-Drinfeld module over $H$ is $$ \delta(h.v) = h_{(1)} v_{(-1)} S(h_{(3)}) \otimes h_{(2)}.v_{(0)}, v \in V, h \in H. $$ Are the two conditions equivalent? Thank you very much.