Yetter-Drinfel’d module
Definition 0.1.
Let be a quasi-bialgebra (http://planetmath.org/Bialgebra) with reassociator . A left -module together with a left -coaction
is called a left Yetter-Drinfeld module if the following equalities hold, for all and
and
and
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 field, which is called an elliptic module. Such modules were first studied by Vladimir Drinfel’d in 1973 and called accordingly
Drinfel’d modules.
References
- 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. http://arxiv.org/PS_cache/math/pdf/0311/0311381v1.pdfMore 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 |