On Hopf algebroid structure of kappa-deformed Heisenberg algebra (CROSBI ID 223759)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Lukierski, Jerzy ; Škoda, Zoran ; Woronowicz, Mariusz
engleski
On Hopf algebroid structure of kappa-deformed Heisenberg algebra
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.
kappa-Minkowski space ; Hopf algebroid ; Heisenberg double
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Podaci o izdanju
80 (3)
2017.
585-585
objavljeno
1063-7788
1562-692X
10.1134/S1063778817030188