§Extensions and quantum Galois theory

• Hypotheses for the extension–algebra correspondence.

• Commutative associative algebra objects, haploidity, and trivial twist.

• Correspondence with VOA extensions.

• Finite-group actions and fixed-point subalgebras.

• Quantum Galois correspondence and its hypotheses.

§9.1 References for expanding the outline

• Yi-Zhi Huang, Alexander Kirillov Jr., and James Lepowsky, Braided tensor categories and extensions of vertex operator algebras.

• Akihide Hanaki, Masahiko Miyamoto, and Daisuke Tambara, Quantum Galois theory for finite groups.

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