Computation of the cohomology rings of Kac-Moody groups, their flag manifolds and classifying spaces

DOI10.1007/s11464-022-1016-zzbMath1497.55006OpenAlexW4280523898MaRDI QIDQ2141330

Yanyan Li

Publication date: 25 May 2022

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-022-1016-z

zbMATH Keywords

classifying spacescohomology ringsspectral sequencesflag manifoldsKac-Moody groups

Mathematics Subject Classification ID

Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Singular homology and cohomology theory (55N10) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02)

Cites Work

• Polynomial invariants of Weyl groups for Kac-Moody groups
• Classifying spaces of Kač-Moody groups
• Cohomology mod 3 of the classifying space BF\(_4\) of thexceptional group F\(_4\)
• The space of loops on a Lie group
• Homology of the Kač-Moody groups. I
• The integral cohomology ring of \(E_{8}/T\)
• Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups
• The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
• On the cohomology mod p of the classifying spaces of the exceptional Lie groups. I
• The integral homology and cohomology rings of \(SO(n)\) and Spin\((n)\)
• Cohomology mod 2 of the classifying space of the compact connected Lie group of type E\(_8\)
• On the cohomology mod 2 of the classifying space of the 1-connected exceptional Lie group \(E_7\)
• The classification of cohomology endomorphisms of certain flag manifolds
• The integral cohomology ring of \(E_7/T\)
• Multiplicative rule of Schubert classes
• Homology of the Kac-Moody groups. II
• The integral cohomology ring of \(F_4/T\) and \(E_6/T\)
• Kac-Moody groups, their flag varieties and representation theory
• Homology of the Kac-Moody groups. III
• Lie algebra cohomology and generalized Schubert cells
• On the topology of Kac-Moody groups
• Cohomology of classifying spaces of central quotients of rank two Kac-Moody groups
• Differential Hopf algebras and the cohomology mod 3 of the compact exceptional groups \(E_ 7\) and \(E_ 8\)
• The cohomology of quotients of classical groups
• On the structure of Hopf algebras
• A new class of Lie algebras
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• Schubert presentation of the cohomology ring of flag manifolds
• T -equivariant K -theory of generalized flag varieties
• Schubert calculus and the Hopf algebra structures of exceptional Lie groups
• An application of the Morse theory to the topology of Lie-groups
• Cohomology mod 3 of the classifying space of the Lie group $E_6$
• Désingularisation des variétés de Schubert généralisées
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• A homotopy construction of the adjoint representation for Lie groups
• On some applications of unstable Adams operations to the topology of Kac-Moody groups
• The cohomology of classifying spaces of 𝐻-spaces
• Cohomology Mod $2$ of the compact exceptional group $E_8$
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
• Homology and Cohomology of Compact Connected Lie Groups
• Sur L'Homologie et la Cohomologie des Groupes de Lie Compacts Connexes
• THE COHOMOLOGY RING OF G/T
• Invariants of Finite Groups Generated by Reflections
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item