Hopf cocycle deformations and invariant theory

Ehud Meir (Corresponding Author)

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Abstract

For a given finite dimensional Hopf algebra H we describe the set of all equivalence classes of cocycle deformations of H as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the Universal Coefficients Theorem in the case of a group algebra, and we also give examples from other families of Hopf algebras, including dual group algebras and Bosonizations of Nichols algebras. In particular, we use the methods developed here to classify the cocycle deformations of a dual pointed Hopf algebra associated to the symmetric group on three letters. We also give an example of a cocycle deformation over a dual group algebra, which has only rational invariants, but which is not definable over the rational field. This differs from the case of group algebras, in which every 2-cocycle is equivalent to one which is definable by its invariants.
Original languageEnglish
Pages (from-to)1355-1395
Number of pages41
JournalMathematische Zeitschrift
Volume294
Early online date13 May 2019
DOIs
Publication statusPublished - Apr 2020

Keywords

  • ALGEBRAS
  • CLASSIFICATION
  • IDENTITIES

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