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 2cocycle is equivalent to one which is definable by its invariants.
Original language  English 

Pages (fromto)  13551395 
Number of pages  41 
Journal  Mathematische Zeitschrift 
Volume  294 
Early online date  13 May 2019 
DOIs  
Publication status  Published  Apr 2020 
Bibliographical note
Open Access via Springer Compact Agreement.The author was supported by the Research Training Group 1670, “Mathematics Inspired by String Theory and Quantum Field Theory”.
Keywords
 ALGEBRAS
 CLASSIFICATION
 IDENTITIES
Fingerprint
Dive into the research topics of 'Hopf cocycle deformations and invariant theory'. Together they form a unique fingerprint.Profiles

Ehud Meir Ben Efraim
 School of Natural & Computing Sciences, Mathematical Science  Senior Lecturer
Person: Academic