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

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dc.contributor.authorFarenick, D.R.
dc.contributor.authorRamsey, Christopher
dc.date.accessioned2020-10-08
dc.date.accessioned2022-05-31T01:15:30Z
dc.date.available2022-05-31T01:15:30Z
dc.date.issued2008
dc.description.abstractThe 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 R , C , or H . 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 π 1 and π 2 of the induced real, complex, and quaternionic pseudospheres.
dc.description.urihttps://library.macewan.ca/full-record/edselp/S0022404908000650
dc.identifier.citationFarenick, D. R. and Ramsey, C. "Unitary groups of nondegenerate Hermitian forms and the homotopy groups of pseudospheres", J. of Pure and Applied Algebra 212 (2008) 2358-2367.
dc.identifier.doihttps://doi.org/10.1016/j.jpaa.2008.03.007
dc.identifier.urihttps://hdl.handle.net/20.500.14078/1804
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjectWitt Extension Theorem
dc.subjecthermitian form
dc.subjecthomotopy groups
dc.subjectfinite-dimensional vector space
dc.titleUnitary groups of nondegenerate Hermitian forms and the homotopy groups of pseudospheres
dc.typeArticle
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