Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

First-order differential calculi over multi-braided quantum groups


A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore, antipodally covariant calculi are studied. The concept of the *-structure on a multi-braided quantum group is formulated, and in particular the structure of left-covariant *-covariant calculi is analyzed. These structures naturally incorporate the idea of the quantum Lie algebra associated to a given multibraded quantum group, the space of left-invariant forms corresponding to the dual of the Lie algebra itself. A special attention is given to differential calculi covariant with respect to the action of the associated braid system. In particular it is shown that the left/right braided-covariance appears as a consequence of the left/right-covariance relative to the group action. Braided counterparts of all basic results of the standard theory are found.


Share this article

50+ Million Readerbase

Journal Highlights

Google Scholar citation report
Citations: 1926

Journal of Generalized Lie Theory and Applications received 1926 citations as per Google Scholar report

Journal of Generalized Lie Theory and Applications peer review process verified at publons

Indexed In

arrow_upward arrow_upward