On Hopf algebroid structure of κ-deformed Heisenberg algebra
- University of Hradec Králové, Faculty of Science (Czech Republic)
- University of Wroclaw, Institute for Theoretical Physics (Poland)
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 (x{sub μ})-hat and corresponding commuting momenta (p{sub μ})-hat . 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.
- OSTI ID:
- 22758683
- Journal Information:
- Physics of Atomic Nuclei, Vol. 80, Issue 3; Other Information: Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7788
- Country of Publication:
- United States
- Language:
- English
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