2017/05/31 by Laiachi El Kaoutit, Paolo Saracco
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Commutative property #Convolution (computer science) #Homeomorphism (graph theory) #Homomorphism #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Lie algebroid #Manifold (fluid mechanics) #Tensor algebra #Tensor product #math.AC #math.AG #math.AT #math.DG #math.RA #msc:13J10 #msc:13N10 #msc:16T15 #msc:16W50 #msc:16W70 #msc:20L05 #msc:22A22 #msc:46M05
paper · pdf · doi:10.1142/s0219199718500153
published as Commun. Contemp. Math. 21 (2019), no. 6, 1850015, 53 pp · Minor changes, 33 pages. To appear in CCM
openalex created_date 2017/05/26 · arxiv created 2018/02/15 · openalex publication_date 2018/04/10 · crossref created 2018/04/10 · crossref issued 2019/08/27 · crossref published 2019/08/27 · crossref published-online 2019/08/27 · crossref deposited 2019/08/27 · crossref published-print 2019/09/01 · arxiv updated 2020/08/12 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/05
Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids between the completion of the finite dual of its universal enveloping Hopf algebroid and the associated convolution algebra. The topological Hopf algebroid structure of this convolution algebra is here clarified, by providing an explicit description of its topological antipode as well as of its other structure maps. Conditions under which that homomorphism becomes an homeomorphism are also discussed. These results, in particular, apply to the smooth global sections of any Lie algebroid over a smooth (connected) manifold and they lead a new formal groupoid scheme to enter into the picture. In the appendices we develop the necessary machinery behind complete Hopf algebroid constructions, which involves also the topological tensor product of filtered bimodules over filtered rings.