Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by Alexander Cardona Pedro Morales Hernán Ocampo Sylvie Paycha & Andrés F. Reyes Lega

Author:Alexander Cardona, Pedro Morales, Hernán Ocampo, Sylvie Paycha & Andrés F. Reyes Lega
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

a structure of left H-comodule , such that

for all and , the following compatibility condition holds:

(4.45)

Thus we have the category of Yetter–Drinfeld modules, with morphisms being linear maps that preserve both the action and the coaction.

Exercise 4.19

Prove that is a braided tensor category, with the tensor product of modules and comodules and braiding

(4.46)

Here is bijective because is so; indeed

(4.47)

That is, the assignment is the categorical version of ; indeed, when H is finite-dimensional, is equivalent to .

Exercise 4.20

Show that is equivalent as tensor category to .

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