arXiv subjects

Tea Martinic

Publications and source records attributed to Tea Martinic.

2 recordsLinked to original sources

arXiv2017

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

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.

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arXiv2015

The Weyl realizations of Lie algebras and left-right duality

We investigate dual realizations of non--commutative spaces of Lie algebra type in terms of formal power series in the Weyl algebra. To each realization of a Lie algebra $\g$ we associate a star--product on the symmetric algebra $S(\g)$ and an ordering on the enveloping algebra $U(\g)$. Dual realizations of $\g$ are defined in terms of left--right duality of the star--products on $S(\g)$. It is shown that the dual realizations are related to an extension problem for $\g$ by shift operators whose action on $U(\g)$ describes left and right shift of the generators of $U(\g)$ in a given monomial. Using properties of the extended algebra, in the Weyl symmetric ordering we derive closed form expressions for the dual realizations of $\g$ in terms of two generating functions for the Bernoulli numbers. The theory is illustrated by considering the $\kappa$--deformed space.

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