caa a22 4500 467882665 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10485-006-9043-6 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9043-6 Cleft Extensions of Hopf Algebroids [Elektronische Daten] [Gabriella Böhm, Tomasz Brzeziński] The notions of a cleft extension and a cross product with a Hopf algebroid are introduced and studied. In particular it is shown that an extension (with a Hopf algebroid ℋ = (ℋ L , ℋ R )) is cleft if and only if it is ℋ R -Galois and has a normal basis property relative to the base ring L of ℋ L . Cleft extensions are identified as crossed products with invertible cocycles. The relationship between the equivalence classes of crossed products and gauge transformations is established. Strong connections in cleft extensions are classified and sufficient conditions are derived for the Chern-Galois characters to be independent on the choice of strong connections. The results concerning cleft extensions and crossed product are then extended to the case of weak cleft extensions of Hopf algebroids hereby defined. Springer Science + Business Media B.V., 2006 Hopf algebroid nationallicence cleft extensions nationallicence cocycles nationallicence comodule algebra nationallicence Böhm Gabriella Research Institute for Particle and Nuclear Physics, P.O.B.49, 1525 Budapest 114, Budapest, Hungary aut Brzeziński Tomasz Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 431-469 0927-2852 14:5-6<431 2006 14 10485 https://doi.org/10.1007/s10485-006-9043-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9043-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Böhm Gabriella Research Institute for Particle and Nuclear Physics, P.O.B.49, 1525 Budapest 114, Budapest, Hungary aut NATIONALLICENCE 700 1- Brzeziński Tomasz Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/5-6(2006-12-01), 431-469 0927-2852 14:5-6<431 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer