Kumar, Shrawan Non-representability of cohomology classes by bi-invariant forms (gauge and Kac-Moody groups). (English) Zbl 0615.57025 Commun. Math. Phys. 106, 177-181 (1986). The author gives a necessary topological condition on a cohomology class of any infinite-dimensional Lie group \(G\), modelled on a Fréchet space, to be representable by a biinvariant form on \(G\). Reviewer: I. V. Chekalov (Minsk) Cited in 1 Document MSC: 57T10 Homology and cohomology of Lie groups 22E67 Loop groups and related constructions, group-theoretic treatment 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Keywords:gauge groups; Kac-Moody groups; cohomology class; infinite-dimensional Lie group; Fréchet space; biinvariant form PDFBibTeX XMLCite \textit{S. Kumar}, Commun. Math. Phys. 106, 177--181 (1986; Zbl 0615.57025) Full Text: DOI References: [1] Atiyah, M. F., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond.A308, 523-615 (1982) · Zbl 0509.14014 [2] Gutkin, E., Slodowy, P.: Cohomologie des variétés de drapeaux infinies. C.R. Acad. Sci. Paris296, 625-627 (1983) · Zbl 0537.14032 [3] Kac, V. G.: Constructing groups associated to infinite-dimensional Lie algebras. MSRI (Springer-Verlag) publications vol. 4 on ?Infinite dimensional groups with applications? 167-216 (1985) [4] Kumar, S.: Rational homotopy theory of flag varieties associated to Kac-Moody groups. MSRI publications vol. 4 (same as in [K]), 233-273 [5] Milnor, J.: Remarks on infinite-dimensional Lie groups. Relativity, groups and topology II, DeWitt, B. S. Stora, R. (eds.). Les Houches, 1009-1057 (1983) [6] Mitter, P. K., Viallet, C. M.: On the bundle of connections and the gauge orbit manifold in Yang-Mills theory. Commun. Math. Phys.79, 457-472 (1981) · Zbl 0474.58004 [7] Uhlenbeck, K.: Connections withL p bounds on curvature. Commun. Math. Phys.83, 31-42 (1982) · Zbl 0499.58019 [8] Warner, F. W.: Foundations of differentiable manifolds and Lie-groups. New York: Scott, Foresman 1971 · Zbl 0241.58001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.