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Induced character in equivariant K-theory, wreath products and pullback of groups
Carácter inducido en K-teoría equivariante, productos wreath y pullbacks de grupos
DOI:
https://doi.org/10.15446/recolma.v56n1.105613Palabras clave:
equivariant K-theory, wreath products, Fock space (en)K-teoría equivariante, productos wreath, espacio de Fock (es)
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Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra
FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C,
defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks of groups. We discuss also some applications of the above result to equivariant connective K-homology.
Sea G un grupo finito y X un G-espacio compacto. En esta nota estudiamos el álgebra (Z+ × Z/2Z)-graduada
FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C,
definida en términos de K-teoría equivariante con respecto a productos guirnalda, como un álgebra simétrica, revisamos algunas de las propiedades de FqG (X) probadas por Segal y Wang. Probamos una formula tipo Kunneth para estas álgebras graduadas, más específcamente, sea H otro grupo finito y Y un H-espacio compacto, nosotros damos una descomposición de FqG × H (X × Y) en términos de FqG (X) y FqH (Y), para esto, debemos estudiar la teoría de representaciones de pullbacks de grupos. Discutimos también algunas aplicaciones de los resultados anteriores a K-homología equivariante conectiva.
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