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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 17 (2021), 041, 20 pages      arXiv:2001.02164      https://doi.org/10.3842/SIGMA.2021.041

A Decomposition of Twisted Equivariant K-Theory

José Manuel Gómez and Johana Ramírez
Escuela de Matemáticas, Universidad Nacional de Colombia, Medellín, Colombia

Received July 13, 2020, in final form April 15, 2021; Published online April 21, 2021

Abstract
For G a finite group, a normalized 2-cocycle αZ2(G,S1) and X a G-space on which a normal subgroup A acts trivially, we show that the α-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 α-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 D2n with n2 an even integer.

Key words: twisted equivariant K-theory; K-theory; finite groups.

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