2012/07/23 by N. Alonso Álvarez, J. M. Fernández Vilaboa, Álvarez, N. Alonso +4
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum many-body systems #math.QA
paper · pdf · doi:10.48550/arxiv.1207.5363
openalex publication_date 2012/07/23 · arxiv created 2012/10/04 · arxiv updated 2012/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we present the general theory of cleft extensions for a cocommutative weak Hopf algebra H. For a weak left H-module algebra we obtain a bijective correspondence between the isomorphisms classes of H-cleft extensions AH\hookrightarrow A, where AH is the subalgebra of coinvariants, and the equivalence classes of crossed systems for H over AH. Finally, we establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group H_φZ(AH)2(H, Z(AH)), where Z(AH) is the center of AH.