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Heisenberg double versus deformed derivatives. (CROSBI ID 155581)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Škoda, Zoran Heisenberg double versus deformed derivatives. // International journal of modern physics A, 26 (2011), 27/28; 4845-4854. doi: 10.1142/S0217751X11054772

Podaci o odgovornosti

Škoda, Zoran

engleski

Heisenberg double versus deformed derivatives.

Two approaches to the tangent space of a noncommutative space whose coordinate algebra is the enveloping algebra of a Lie algebra are known: the Heisenberg double construction and the approach via deformed derivatives, usually defined by procedures involving orderings among noncommutative coordinates or equivalently involving realizations via formal differential operators. In an earlier work, we rephrased the deformed derivative approach introducing certain smash product algebra twisting a semicompleted Weyl algebra. We show here that the Heisenberg double in the Lie algebra case, is isomorphic to that product in a nontrivial way, involving a datum $\phi$ parametrizing the orderings or realizations in other approaches. This way, we show that the two different formalisms, used by different communities, for introducing the noncommutative phase space for the Lie algebra type noncommutative spaces are mathematically equivalent.

universal enveloping algebra; Hopf algebra; deformed derivative; Heisenberg double

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Podaci o izdanju

26 (27/28)

2011.

4845-4854

objavljeno

0217-751X

10.1142/S0217751X11054772

Povezanost rada

Fizika, Matematika

Poveznice
Indeksiranost