Locally convex bialgebroid of an action Lie groupoid

Kališnik, Jure (author)

Action Lie groupoids are used to model spaces of orbits of actions of Lie groups on manifolds. For each such action groupoid $M\rtimes H$ we construct a locally convex bialgebroid $\mathord{\mathrm{Dirac}}(M\rtimes H)$ with an antipode over $\mathord{\mathcal{C}^{\infty}_{c}}(M)$, from which the groupoid $M\rtimes H$ can be reconstructed as its spectral action Lie groupoid $\mathord{\mathcal{AG}_{\mathit{sp}}}(\mathord{\mathrm{Dirac}}(M\rtimes H))$.

• Language: English
• Keywords: action Lie groupoid, coalgebra, Dirac distribution, Hopf algebroid, transversal distribution
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 28 str.
• Numbering: Vol. 21, iss. 1, art. 17
• PID: 20.500.12556/RUL-154378
• UDC: 512
• ISSN on article: 1660-5446
• DOI: 10.1007/s00009-023-02552-6
• COBISS.SI-ID: 183763459
• Publication date in RUL: 12.02.2024

Record is a part of a journal

• Title: Mediterranean journal of mathematics
• Shortened title: Mediterr. j. math.
• Publisher: Springer Nature
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.