Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups

DOI10.1007/BF01388548zbMath0566.57028WikidataQ115393645 ScholiaQ115393645MaRDI QIDQ1059312

Victor G. Kac

Publication date: 1985

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143219

zbMATH Keywords

Weyl grouproot systemChow ringcohomology of compact Lie groupscomplex algebraic groupspectral sequence of fibration

Mathematics Subject Classification ID

Classical groups (algebro-geometric aspects) (14L35) Cohomology theory for linear algebraic groups (20G10) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Serre spectral sequences (55T10)

Related Items

Motivic construction of cohomological invariants, Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras, Computation of the cohomology rings of Kac-Moody groups, their flag manifolds and classifying spaces, Canonicalp-dimensions of algebraic groups and degrees of basic polynomial invariants, Schubert calculus and the Hopf algebra structures of exceptional Lie groups, Parity sheaves, Schubert presentation of the cohomology ring of flag manifolds, Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group, The \(J\)-invariant and Tits algebras for groups of inner type \(E_6\), The \(J\)-invariant, Tits algebras and triality., The Chow ring of the symmetric space \(\mathrm{GL}(2n,\mathbb C)/\mathrm{SO}(2n,\mathbb C)\), Correlation functions from two-dimensional string Ward identities, Quotient spaces of compact Lie groups by tori, Exact solution of a boundary conformal field theory, The integral homology and cohomology rings of \(SO(n)\) and Spin\((n)\), On the topology of Kac-Moody groups, Décompositions dans l'algèbre des différences divisées. (Decompositions in the algebra of divided differences), Equivariant pretheories and invariants of torsors, Generically split projective homogeneous varieties, Integral weyl invariants and the borel homomorphism for spin(n), The Tits indices over semilocal rings., The Chow rings of generalized Grassmannians, Gerbal central extensions of reductive groups by \(\mathcal{K}_3\), Hopf-theoretic approach to motives of twisted flag varieties, Variations on the cohomology of loop spaces on generalized homogeneous spaces, Twisted quadratic foldings of root systems, Generically split projective homogeneous varieties. II

Cites Work

• Infinite dimensional Lie algebras. An introduction
• Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes
• Two torsion and the loop space conjecture
• Hopf algebra structure of mod 2 cohomology of simple Lie groups
• On the cohomology mod 2 of \(E_ 8\)
• Differential Hopf algebras and the cohomology mod 3 of the compact exceptional groups \(E_ 7\) and \(E_ 8\)
• Ideals generated by \(R\)-sequences
• The cohomology of quotients of classical groups
• Some arithmetical results on semi-simple Lie algebras
• Invariants symétriques entiers des groupes de Weyl et torsion
• The topology of rotation groups
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Cohomology Mod $2$ of the compact exceptional group $E_8$
• The Betti Numbers of the Simple Lie Groups
• On Differential Hopf Algebras
• Sur L'Homologie et la Cohomologie des Groupes de Lie Compacts Connexes
• Unnamed Item
• Unnamed Item
• Unnamed Item