Unitary groups of nondegenerate Hermitian forms and the homotopy groups of pseudospheres

• Autores: Douglas Farenick, Christopher Ramsey
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 10, 2008, págs. 2358-2367
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2008.03.007
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• Resumen

  • The Witt Extension Theorem states that the unitary group of a finite-dimensional vector space V equipped with a nondegenerate hermitian form acts transitively on the pseudosphere induced by the form. We provide a new, constructive proof of this result for finite-dimensional vector spaces V over , , or . This constructive proof is then used to prove a similar result for the unitary group of a finitely generated free right module over an abelian AW*-algebra. The topology of these unitary groups is examined and as an application we determine the homotopy groups p1 and p2 of the induced real, complex, and quaternionic pseudospheres.