Induced character in equivariant K-theory, wreath products and pullback of groups

German Combariza; Juan Rodriguez; Mario Velasquez

doi:10.15446/recolma.v56n1.105613

Publicado

2022-11-02

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.v56n1.105613

Palabras clave:

equivariant K-theory, wreath products, Fock space (en)
K-teoría equivariante, productos wreath, espacio de Fock (es)

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Autores/as

German Combariza Fundación Universitaria Konrad Lorenz
Juan Rodriguez École Normale Supérieure de Lyon
Mario Velasquez Universidad Nacional de Colombia

Resumen (en)
Resumen (es)

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

F^q_G (X) = ⊕_{n ≤ 0} qⁿ · K_{G∫G_n}(Xⁿ) ⊗ C,

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.

Sea G un grupo finito y X un G-espacio compacto. En esta nota estudiamos el álgebra (Z₊ × Z/2Z)-graduada

F^q_G (X) = ⊕_{n ≤ 0} qⁿ · K_G∫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 F^q_G (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 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.

Referencias

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Cómo citar

APA

Combariza, G., Rodriguez, J. y Velasquez, M. (2022). Induced character in equivariant K-theory, wreath products and pullback of groups. Revista Colombiana de Matemáticas, 56(1), 35–61. https://doi.org/10.15446/recolma.v56n1.105613

ACM

[1]

Combariza, G., Rodriguez, J. y Velasquez, M. 2022. Induced character in equivariant K-theory, wreath products and pullback of groups. Revista Colombiana de Matemáticas. 56, 1 (nov. 2022), 35–61. DOI:https://doi.org/10.15446/recolma.v56n1.105613.

ACS

(1)

Combariza, G.; Rodriguez, J.; Velasquez, M. Induced character in equivariant K-theory, wreath products and pullback of groups. rev.colomb.mat 2022, 56, 35-61.

ABNT

COMBARIZA, G.; RODRIGUEZ, J.; VELASQUEZ, M. Induced character in equivariant K-theory, wreath products and pullback of groups. Revista Colombiana de Matemáticas, [S. l.], v. 56, n. 1, p. 35–61, 2022. DOI: 10.15446/recolma.v56n1.105613. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/105613. Acesso em: 9 mar. 2025.

Chicago

Combariza, German, Juan Rodriguez, y Mario Velasquez. 2022. «Induced character in equivariant K-theory, wreath products and pullback of groups». Revista Colombiana De Matemáticas 56 (1):35-61. https://doi.org/10.15446/recolma.v56n1.105613.

Harvard

Combariza, G., Rodriguez, J. y Velasquez, M. (2022) «Induced character in equivariant K-theory, wreath products and pullback of groups», Revista Colombiana de Matemáticas, 56(1), pp. 35–61. doi: 10.15446/recolma.v56n1.105613.

IEEE

[1]

G. Combariza, J. Rodriguez, y M. Velasquez, «Induced character in equivariant K-theory, wreath products and pullback of groups», rev.colomb.mat, vol. 56, n.º 1, pp. 35–61, nov. 2022.

MLA

Combariza, G., J. Rodriguez, y M. Velasquez. «Induced character in equivariant K-theory, wreath products and pullback of groups». Revista Colombiana de Matemáticas, vol. 56, n.º 1, noviembre de 2022, pp. 35-61, doi:10.15446/recolma.v56n1.105613.

Turabian

Combariza, German, Juan Rodriguez, y Mario Velasquez. «Induced character in equivariant K-theory, wreath products and pullback of groups». Revista Colombiana de Matemáticas 56, no. 1 (noviembre 2, 2022): 35–61. Accedido marzo 9, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/105613.

Vancouver

1.

Combariza G, Rodriguez J, Velasquez M. Induced character in equivariant K-theory, wreath products and pullback of groups. rev.colomb.mat [Internet]. 2 de noviembre de 2022 [citado 9 de marzo de 2025];56(1):35-61. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/105613