Geodesic
Criterion for the extendability of a unitary character on a normal subgroup of a product group to a pure one-dimensional pseudorepresentation of the group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 251-254
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We prove a criterion for a given unitary character on a normal subgroup of a group that is a product of this normal subgroup and some subgroup to have an extension to a pure one-dimensional pseudorepresentation of the whole group. 
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A. I. Shtern. Criterion for the extendability of a unitary character on a normal subgroup of a product group to a pure one-dimensional pseudorepresentation of the group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 251-254. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a14/

[1] Shtern A. I., “Spetsificheskie svoistva odnomernykh psevdopredstavlenii grupp”, Fundament. i prikl. matem., 21:1 (2016), 247–255 | MR

[2] Shtern A. I., “Lokalno ogranichennye finalno prednepreryvnye konechnomernye kvazipredstavleniya svyaznykh lokalno kompaktnykh grupp”, Matem. sb., 208:10 (2017), 149–170 | DOI | MR | Zbl

[3] Shtern A. I., “Quasi-symmetry. I”, Russ. J. Math. Phys., 2:3 (1994), 353–382 | MR | Zbl

[4] Shtern A. I., “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751 | DOI | MR | Zbl

[5] Shtern A. I., “Extension of pseudocharacters from normal subgroups”, Proc. Jangjeon Math. Soc., 18:4 (2015), 427–433 | MR | Zbl

[6] Shtern A. I., “Extension of characters on the normal subgroup of a semi-direct product group to one-dimensional pseudorepresentations of the group”, Proc. Jangjeon Math. Soc., 19:3 (2016), 451–455 | MR | Zbl

[7] Shtern A. I., “Extension of pseudocharacters from normal subgroups. II”, Proc. Jangjeon Math. Soc., 19:2 (2016), 213–218 | MR | Zbl

[8] Shtern A. I., “Extension of pseudocharacters from normal subgroups. III”, Proc. Jangjeon Math. Soc., 19:4 (2016), 609–614 | MR | Zbl

[9] Shtern A. I., “Corrections to «Extensions of characters from the normal subgroup of a semidirect product group to one-dimensional pseudorepresentations of the group»”, Proc. Jangjeon Math. Soc., 20:2 (2017), 313–317 | MR | Zbl

[10] Shtern A. I., “A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups”, Izv. Math., 72:1 (2008), 169–205 | DOI | MR | Zbl