1-Cycle Deformations for Yetter-Drinfeld Coalgebras
Abstract
Abstract For a quasi-Hopf algebra H , we study two types of 1-cycle deformations for a coalgebra C within the category of Yetter-Drinfeld modules over H , $${}_H^H{\mathcal YD}$$ H H Y D . The two deformations produce C -comodule structures in $${}_H^H{\mathcal YD}$$ H H Y D and new coalgebra structures on C in $${}_H^H{\mathcal YD}$$ H H Y D , respectively. We show that the isomorphism types of these structures are described by a 1-homology $${\mathcal H}^1_H(C, H_0)$$ H H 1 ( C , H 0 ) that we will introduce. Then we apply our results to the so called symplectic fermion quasi-Hopf algebras, algebras recently introduced by Farsad, Gainutdinov and Runkel.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Algebras and Representation Theory
- Volume
- 29
- Issue
- 2
- Pages
- 279–329
- Publication date
- 11 March 2026
- Language
- EN