### Abstract

Original language | English |
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Journal | Mathematische Zeitschrift |

Early online date | 13 May 2019 |

DOIs | |

Publication status | E-pub ahead of print - 13 May 2019 |

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### Cite this

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

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Hopf cocycle deformations and invariant theory

AU - Meir, Ehud

N1 - 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”.

PY - 2019/5/13

Y1 - 2019/5/13

N2 - 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.

AB - 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.

UR - http://www.mendeley.com/research/hopf-cocycle-deformations-invariant-theory

U2 - 10.1007/s00209-019-02326-5

DO - 10.1007/s00209-019-02326-5

M3 - Article

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

ER -