First-Order Differential Calculi Over Multi-Braided Quantum Groups

Details First-Order Differential Calculi Over Multi-Braided Quantum Groups First-Order Differential Calculi Over Multi-Braided Quantum Groups

1996-05-05

arxiv.org/abs/q-alg/9605006v1

Mathematics

Quantum Algebra

32 pages, AMS-LaTeX/1, this is the revised version of an unpublished `92 article

Scientific paper

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. 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.

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