Some Infinite Dimensional Groups and Bundles

  • Alan L. Carey

    The Australian National University, Canberra, Australia


The group O of Bogoliubov automorphisms of the infinite dimensional Clifford algebra, implementable in a Fock representation, the analogous group of automorphisms of the canonical commutation relations and various generalisations are discussed. Their homotopy type is determined in a topology naturally defined by the spin and metaplectic representations. A theorem of Araki and Evans on a 2-index for certain projections is generalised using our "mod 2" index for ???. Connections with _K_1 of certain Banach algebras are described.

Cite this article

Alan L. Carey, Some Infinite Dimensional Groups and Bundles. Publ. Res. Inst. Math. Sci. 20 (1984), no. 6, pp. 1103–1117

DOI 10.2977/PRIMS/1195180373