Yetter-Drinfel’d module

Definition 0.1.

Let H be a quasi-bialgebra ( with reassociator Φ. A left H-module M together with a left H-coaction λM:MHM,


is called a left Yetter-Drinfeld module if the following equalities hold, for all hH and mM:






Remark: This module (ref.[1]) is essential for solving the quasi-Yang-Baxter equation which is an important relation in Mathematical Physics.
Drinfel’d modules: Let us consider a module that operates over a ring of functions on a curve over a finite fieldMathworldPlanetmath, which is called an elliptic module. Such modules were first studied by Vladimir Drinfel’d in 1973 and called accordingly Drinfel’d modules.


  • 1 Bulacu, D, Caenepeel, S, Torrecillas, B, Doi-Hopf modules and Yetter-Drinfeld modules for quasi-Hopf algebras. Communications in Algebra, 34 (9), pp. 3413-3449, 2006.
  • 2 D. Bulacu, S. Caenepeel, A and F. Panaite. 2003. Properties of Yetter-Drinfeld modules over Quasi-Hopf Algebras., Preprint.
Title Yetter-Drinfel’d module
Canonical name YetterDrinfeldModule
Date of creation 2013-03-22 18:24:15
Last modified on 2013-03-22 18:24:15
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 19
Author bci1 (20947)
Entry type Definition
Classification msc 57T05
Classification msc 13-00
Classification msc 81R50
Classification msc 81R15
Classification msc 46L05
Classification msc 16W30
Synonym Drinfel’d module
Synonym quasi-bialgebra
Related topic QuantumGroups
Related topic Module
Related topic GrassmannHopfAlgebroidCategoriesAndGrassmannCategories
Related topic GrassmanHopfAlgebrasAndTheirDualCoAlgebras
Related topic C_cG
Related topic LocallyCompact
Related topic LocallyCompactGroupoids
Related topic WeakHopfCAlgebra2
Related topic Bialgebra
Related topic ExampleOfModule2
Defines H-module
Defines bialgebras