Naslov
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

Autori
Meljanac, Stjepan ; Krešić-Jurić, Saša ; Martinić, Tea

Izvornik
Journal of mathematical physics (0022-2488) 58 (2017); 071701-1

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

Ključne riječi
non-commutative spaces ; bicovariant differential calculus ; Lie superalgebras ; realizations

Sažetak
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra $\g_0$ we construct a Lie superalgebra $\g=\g_0\oplus \g_1$ containing noncommutative coordinates and one--forms. We show that $\g$ can be extended by a set of generators $T_{; ; ; AB}; ; ; $ whose action on the enveloping algebra $U(\g)$ gives the commutation relations between monomials in $U(\g_0)$ and one--forms. Realizations of noncommutative coordinates, one--forms and the generators $T_{; ; ; AB}; ; ; $ as formal power series in a semicompleted Weyl superalgebra are found. In the special case $\dim(\g_0)= \dim(\g_1)$ we also find a realization of the exterior derivative on $U(\g_0)$. The realizations of these geometric objects yield a bicovariant differential calculus on $U(\g_0)$ as a deformation of the standard calculus on the Euclidean space.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

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