Hopf cocycle deformations and invariant theory

Ehud Meir (Corresponding Author)

Research output: Contribution to journalArticle

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
JournalMathematische Zeitschrift
Early online date13 May 2019
DOIs
Publication statusE-pub ahead of print - 13 May 2019

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Invariant Theory
Deformation Theory
Cocycle
Group Algebra
Hopf Algebra
Dual Group
Geometric Invariant Theory
Bosonization
Invariant
Finite Dimensional Algebra
Equivalence class
Symmetric group
Classify
Algebra
Coefficient
Theorem

Cite this

Hopf cocycle deformations and invariant theory. / Meir, Ehud (Corresponding Author).

In: Mathematische Zeitschrift, 13.05.2019.

Research output: Contribution to journalArticle

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