Vol. 305, No. 2, 2020

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The rational cohomology Hopf algebra of a generic Kac–Moody group

Zhao Xu-an and Gao Hongzhu

Vol. 305 (2020), No. 2, 757–766
DOI: 10.2140/pjm.2020.305.757
Abstract

In this paper we determine the rational homotopy type of the classifying space of a generic Kac–Moody group by computing its rational cohomology ring. As an application we determine the rational homology Hopf algebra of the generic Kac–Moody group.

Keywords
Kac–Moody group, classifying space, Hopf algebra
Mathematical Subject Classification 2010
Primary: 55N45
Milestones
Received: 15 April 2018
Revised: 2 April 2019
Accepted: 4 November 2019
Published: 29 April 2020
Authors
Zhao Xu-an
School of Mathematical Sciences
Beijing Normal University
Key Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing
China
Gao Hongzhu
School of Mathematical Sciences
Beijing Normal University
Key Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing
China