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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 041, 20 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.041
(Mi sigma1724)
 

A Decomposition of Twisted Equivariant $K$-Theory

José Manuel Gómez, Johana Ramírez

Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia
References:
Abstract: For $G$ a finite group, a normalized $2$-cocycle $\alpha\in Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as a direct sum of twisted equivariant $K$-theories of $X$ parametrized by the orbits of an action of $G$ on the set of irreducible $\alpha$-projective representations of $A$. This generalizes the decomposition obtained in [Gómez J.M., Uribe B., Internat. J. Math. 28 (2017), 1750016, 23 pages, arXiv:1604.01656] for equivariant $K$-theory. We also explore some examples of this decomposition for the particular case of the dihedral groups $D_{2n}$ with $n\ge 2$ an even integer.
Keywords: twisted equivariant $K$-theory, $K$-theory, finite groups.
Funding agency Grant number
Ministerio de Ciencia Tecnología e Innovación FP44842-013-201
727
The first author acknowledges and thanks the financial support provided by MINCIENCIAS through grant number FP44842-013-2018 of the Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación. The second author acknowledges and thanks the financial support provided by MINCIENCIAS through grant number 727 of the program Doctorados nacionales 2015 of the Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación.
Received: July 13, 2020; in final form April 15, 2021; Published online April 21, 2021
Bibliographic databases:
Document Type: Article
MSC: 19L50, 19L47
Language: English
Citation: José Manuel Gómez, Johana Ramírez, “A Decomposition of Twisted Equivariant $K$-Theory”, SIGMA, 17 (2021), 041, 20 pp.
Citation in format AMSBIB
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\by Jos\'e~Manuel~G\'omez, Johana~Ram{\'\i}rez
\paper A Decomposition of Twisted Equivariant $K$-Theory
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\yr 2021
\vol 17
\papernumber 041
\totalpages 20
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\crossref{https://doi.org/10.3842/SIGMA.2021.041}
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