Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/fs-coalgebras-and-crossed-coproducts-KanGeAnW9s
References (20)
-
U. Kraehmer, F. Wagemann (2014)
Racks, Leibniz algebras and Yetter–Drinfel'd modulesGeorgian Mathematical Journal, 22
-
G. Militaru (1998)
The Long Dimodules Category and Nonlinear EquationsAlgebras and Representation Theory, 2
-
Akira Masuoka, Yukio Doi (1992)
Genaralization fo cleft comodule algabrasCommunications in Algebra, 20
-
S. Caenepeel, S. Dascalescu, G. Militaru, F. Panaite (1997)
Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproductsBulletin of The Belgian Mathematical Society-simon Stevin, 4
-
S. Montgomery (1993)
Hopf algebras and their actions on rings -
Liangyun Zhang (2006)
Long Bialgebras, Dimodule Algebras and Quantum Yang–Baxter Modules over Long BialgebrasActa Mathematica Sinica, 22
-
Lowell Abrams (1998)
Modules, Comodules, and Cotensor Products over Frobenius AlgebrasJournal of Algebra, 219
-
Lowell Abrams (1996)
TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND FROBENIUS ALGEBRASJournal of Knot Theory and Its Ramifications, 05
-
S. Caenepeel, G. Militaru, Shenglin Zhu (1997)
DOI-HOPF MODULES, YETTER-DRINFEL'D MODULES AND FROBENIUS TYPE PROPERTIESTransactions of the American Mathematical Society, 349
-
Allen Bell, Rolf Farnsteiner (1993)
On the theory of Frobenius extensions and its application to Lie superalgebrasTransactions of the American Mathematical Society, 335
-
K. Beidar, Y. Fong, A. Stolin (1997)
On Antipodes and Integrals in Hopf Algebras over Rings and the Quantum Yang-Baxter EquationJournal of Algebra, 194
-
B. Tilson (2019)
ModulesInt. J. Algebra Comput., 20
-
S. Caenepeel, G. Militaru, Shenglin Zhu (2002)
Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations -
Charles StreetBaltimore (1996)
Two-dimensional Topological Quantum Field Theories and Frobenius Algebras -
S. Dascalescu, C. Nastasescu, S. Raianu (2001)
Hopf algebras : an introduction -
(1977)
Semiperfect coalgebras -
Davida Fischman, S. Montgomery, H. Schneider (1997)
Frobenius extensions of subalgebras of Hopf algebrasTransactions of the American Mathematical Society, 349
-
S. Caenepeel, B. Ion, G. Militaru (1998)
The structure of Frobenius algebras and separable algebrasarXiv: Quantum Algebra
-
A. Nakajima (1975)
On generalized Harrison cohomology and Galois objectMathematical journal of Okayama University, 17
-
K. Beidar, Y. Fong, A. Stolin (1997)
On Frobenius algebras and the quantum Yang-Baxter equationTransactions of the American Mathematical Society, 349
- Publisher
- de Gruyter
- Copyright
- © 2019 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 1572-9176
- eISSN
- 1572-9176
- DOI
- 10.1515/gmj-2017-0037
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn this paper, we introduce FS-coalgebras, which provide solutionsof FS-equations and also solution ofbraid equations considered by Caenepeel, Militaru and Zhu.FS-coalgebras are constructed by usingFS-equations and Harrison cocycles.As applications, we prove that every bialgebraH is an FS-bialgebra if and only if there is atwo-sided integral α in H∗{H^{\ast}}such thatε(α)=1{\varepsilon(\alpha)=1}, and we show thatthe crossed coproduct HR{H^{R}}introduced by the Harrison cocycle R is anFS-coalgebra when (H,R){(H,R)}is a finite-dimensional quasitriangular Hopfalgebra or a Long copaired bialgebra.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2019