Categorification at prime roots of unity and hopfological finiteness

Abstract

We survey some recent results in hopfological algebra and the program of categorification at prime roots of unity. A categorical Jones-Wenzl projector at prime roots of unity is studied, and it is shown that this projector is hopfologically finite in special characteristics, while generically it is infinite.2010 Mathematics Subject Classification. Primary 81R50; Secondary 16E20, 16E35. Key words and phrases. Categorification, hopfological algebra, prime roots of unity. The authors are very grateful to Mikhail Khovanov for his support and encouragement, as well as sharing with us his insights on the subject. The authors would also like to thank Catharina Stroppel for helpful discussions about categorifying Jones-Wenzl projectors.

On some p–differential graded link homologies, II

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“…@ p / (hence the word "hopfological"). We refer the reader to [10] for a survey of some recent progress in this direction.…”

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“…The theory has since been applied to categorify various root-ofunity forms of quantum groups. We refer the reader to [25] for a brief summary and special phenomena at a p-th root of unity.…”

On some p-differential graded link homologies

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