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  • 1- Fakülteler | Faculties
  • Fen Edebiyat Fakültesi / Faculty of Arts and Sciences
  • Matematik Bölümü / Department of Mathematics
  • FEF - Makale Koleksiyonu | Matematik Bölümü / Department of Mathematics
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Topological Hopf algebras and their Hopf-cyclic cohomology

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Date

2019-01-29

Author

Rangipour, Bahram
Sütlü, Serkan Selçuk

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Citation

Rangipour, B. & Sütlü, S. S. (2019). Topological hopf algebras and their hopf-cyclic cohomology. Communications in Algebra, 47(4), 1490-1515. doi:10.1080/00927872.2018.1508581

Abstract

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of coefficients (AYD modules) over a topological Lie algebra and those over its universal enveloping (Hopf) algebra are isomorphic. For topological Hopf algebras, the category of coefficients is identified with the representation category of a topological algebra called the anti-Drinfeld double. Finally, a topological van Est type isomorphism is detailed, connecting the Hopf-cyclic cohomology to the relative Lie algebra cohomology with respect to a maximal compact subalgebra.

Source

Communications in Algebra

Volume

47

Issue

4

URI

https://hdl.handle.net/11729/1587
http://dx.doi.org/10.1080/00927872.2018.1508581

Collections

  • FEF - Makale Koleksiyonu | Matematik Bölümü / Department of Mathematics [215]
  • Scopus İndeksli Makale Koleksiyonu [880]
  • WoS İndeksli Makale Koleksiyonu [892]



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