2014/05/13 by Tomasz Brzeziński, Brzeziński, Tomasz
Mathematics · #16S38 #58B32 #58B34 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16S38 #msc:58B32 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1405.3105
13 pages; final version accepted by Algebras and Representation Theory
openalex publication_date 2014/05/13 · arxiv created 2015/07/21 · arxiv updated 2015/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Strongly ℤ-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q, 0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q, 0) and the isomorphism classes of sections of associated line bundles over B(p;q, 0) is computed thus demonstrating that these bundles, which are labeled by integers, are non-trivial and mutually non-isomorphic. The constructed strongly ℤ-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong.