Jos´e Nicanor ALVAREZ ALONSO, Jos´e Manuel VILABOA FERNANDEZ, Ramon RODRIGUEZ GONZALEZ

Coextended weak entwining structures

In this paper, we formulate the definition of coextended weak entwining structure in a strict monoidal category with equalizers. For a coextended weak entwining structure (A,D,y,a), we introduce the notions of weak (D,a)-cleft extension and weak (D,a)-Galois extension (with normal basis), proving that weak (D,a)-Galois extensions with normal basis are equivalent to weak (D,a)-cleft extensions.

Anahtar Kelimeler:

Monoidal category, coextended weak entwining structure, weak cleft extension, weak Galois extension, normal basis

Coextended weak entwining structures

Keywords:

Monoidal category, coextended weak entwining structure, weak cleft extension, weak Galois extension, normal basis,

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l] Alonso Alvarez JN, Fernandez Vilaboa J M, Gonzalez Rodriguez R, Rodriguez Raposo AB. Weak C-cleft extensions, weak entwining structures and weak Hopf algebras. J Algebra 2005; 284: 6797704.
Alonso Alvarez JN, Fernandez Vilaboa JM, Gonzalez Rodriguez R, Rodriguez Raposo AB. Weak C-cleft extensions and weak Galois extensions. J Algebra 2006; 299: 2767293.
Alonso Alvarez JN, Fernandez Vilaboa JM, Gonzalez Rodriguez R, Soneira Calvo C. Lax entwining structures, groupoid algebras and cleft extensions. Bull Brazilian Math Soc 2014; 45: 133—178.
Böhm G, Nill F, Szlachanyi K. Weak Hopf algebras, I. Integral theory and C* —structure. J Algebra 1999; 221: 385—438.
EE Brzezinski T. On modules associated to coalgebra Galois extensions. J Algebra 1999; 215: 290—317.
EEE Brzezinski T, Majid S. Coalgebra bundles. Com Math Phys 1998; 191: 4674192.
Doi Y, Takeuchi M. Cleft comodule algebras for a bialgebra. Comm Algebra 1986; 14: 801—817.
Fernandez Vilaboa JM, Gonzalez Rodriguez R, Rodriguez Raposo AB. Preunits and weak crossed products. J Pure
Fernandez Vilaboa JM, Gonzalez Rodriguez R, Rodriguez Raposo AB. Weak crossed biproducts and weak projec
tions. Sci China Math 2012; 55: 1321—1526.
Fernandez Vilaboa JM, Villanueva Novoa, E. A characterization of the cleft comodule triples. Comm Algebra 1988; 16: 613—622.
Kreimer HF, Takeuchi M. Hopf algebras and Galois extensions of an algebra. Indiana Univ Math J 1981; 30: 675—691.
Mackenzie S. Double Lie algebroids and second—order geometry 1. Adv Math 1992; 94: 180—239.