Naslov
On Hopf algebroid structure of kappa-deformed Heisenberg algebra

Autori
Lukierski, Jerzy ; Škoda, Zoran ; Woronowicz, Mariusz

Izvornik
Physics of atomic nuclei (1063-7788) 80 (2017), 3; 585-585

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
kappa-Minkowski space ; Hopf algebroid ; Heisenberg double

Sažetak
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 xμˆ and corresponding commuting momenta pμˆ. 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

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