Real C*-Algebras, United K-Theory, and the Kunneth Formula

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dc.creatorBoersema, Jeffrey L.
dc.date2002-08-08
dc.date.accessioned2026-07-07T04:50:08Z
dc.date.available2026-07-07T04:50:08Z
dc.descriptionWe define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -- real K-theory, complex K-theory, and self-conjugate K-theory -- and the natural transformations among them. The advantage of united K-theory over ordinary K-theory lies in its homological algebraic properties, which allow us to construct a Kunneth-type, non-splitting, short exact sequence whose middle term is the united K-theory of the tensor product of two real C*-algebras A and B which holds as long as the complexification of A is in the bootstrap category. Since united K-theory contains ordinary K-theory, our sequence provides a way to compute the K-theory of the tensor product of two real C*-algebras. As an application, we compute the united K-theory of the tensor product of two real Cuntz algebras. Unlike in the complex case, it turns out that the isomorphism class of the tensor product O_{k+1} otimes O_{l+1} is not determined solely by the greatest common divisor of k and l. Hence we have examples of non-isomorphic, simple, purely infinite, real C*-algebras whose complexifications are isomorphic.
dc.description67 pages, 13 tables, uses xy-pic for commutative diagrams, to appear in "K-theory"
dc.identifierhttps://arxiv.org/abs/math/0208068
dc.identifierhttp://arxiv.org/abs/math/0208068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64686
dc.subjectOperator Algebras
dc.subjectK-Theory and Homology
dc.titleReal C*-Algebras, United K-Theory, and the Kunneth Formula
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