On Hopf algebroid structure of κ-deformed Heisenberg algebra
- Авторы: Lukierski J.1, Škoda Z.2, Woronowicz M.1
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Учреждения:
- Institute for Theoretical Physics
- Faculty of Science
- Выпуск: Том 80, № 3 (2017)
- Страницы: 576-585
- Раздел: Elementary Particles and Fields Theory
- URL: https://journals.rcsi.science/1063-7788/article/view/192017
- DOI: https://doi.org/10.1134/S1063778817030188
- ID: 192017
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Аннотация
The (4 + 4)-dimensional κ-deformed quantum phase space as well as its (10 + 10)-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the (10 + 10)-dimensional quantum phase space is the double of D = 4 κ-deformed Poincaré Hopf algebra H and the standard (4 + 4)-dimensional space is its subalgebra generated by κ-Minkowski coordinates \(\widehat {{x_\mu }}\) and corresponding commuting momenta \(\widehat {{p_\mu }}\). Every Heisenberg double appears as the total algebra of a Hopf algebroid over a base algebra which is in our case the coordinate sector. We exhibit the details of this structure, namely the corresponding right bialgebroid and the antipode map. We rely on algebraic methods of calculation in Majid–Ruegg bicrossproduct basis. The target map is derived from a formula by J.-H. Lu. The coproduct takes values in the bimodule tensor product over a base, what is expressed as the presence of coproduct gauge freedom.
Об авторах
J. Lukierski
Institute for Theoretical Physics
Автор, ответственный за переписку.
Email: jerzy.lukierski@ift.uni.wroc.pl
Польша, Wroclaw
Z. Škoda
Faculty of Science
Email: jerzy.lukierski@ift.uni.wroc.pl
Чехия, Hradec Králové
M. Woronowicz
Institute for Theoretical Physics
Email: jerzy.lukierski@ift.uni.wroc.pl
Польша, Wroclaw
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