Abstract
In the theory of dynamical Yang–Baxter equation, with any Hopf algebra H, a certain H-module, and H-comodule algebra L (base algebra) one can associate a monoidal category. Given an algebra A in that category, one can construct an associative algebra A ⋊ L, which is a generalization of the ordinary smash product when A is an ordinary H-algebra. We study this “dynamical smash product” and its modules induced from one-dimensional representations of the subalgebra L. In particular, we construct an analog of the Galois map A ⊗ A H A → A ⊗ H* and define dynamical Galois extensions.
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