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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.56 no.1 Bogotá jan./jun. 2022 Epub 03-Jan-2023
https://doi.org/10.15446/recolma.v56n1.105613
Original articles
Induced character in equivariant K-theory, wreath products and pullback of groups
Carácter inducido en K-teoría equivariante, productos wreath y pullbacks de grupos
1 Fundación Universitaria Konrad Lorenz, Bogotá, Colombia
2 École normale supérieure de Lyon, Lyon, France
3 Universidad Nacional de Colombia, Bogotá, Colombia
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
defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of F q G (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 F q G(H (X ( Y) in terms of F q G (X) and F q H (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.
Keywords: equivariant K-theory; wreath products; Fock space
Sea G un grupo finito y X un G-espacio compacto. En esta nota estudiamos el álgebra (Z + ( Z /2Z)-graduada
Definida en términos de K-teoría equivariante con respecto a productos guirnalda, como un álgebra simétrica, revisamos algunas de las propiedades de F q G (X) probadas por Segal y Wang. Probamos una formula tipo Kunneth para estas álgebras graduadas, más específicamente, sea H otro grupo finito y Y un H-espacio compacto, nosotros damos una descomposición de F q G(H (X(Y) en términos de F q G (X) y F q H (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.
Palabras clave: K-teoría equivariante; productos wreath; espacio de Fock
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Received: November 01, 2021; Accepted: May 27, 2022
This is an open-access article distributed under the terms of the Creative Commons Attribution License
