Induced extended calculus on the quantum plane

Details Induced extended calculus on the quantum plane Induced extended calculus on the quantum plane

1994-01-28

arxiv.org/abs/hep-th/9401141v1

Alg.Anal. 6 (1994) 252

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

The non-commutative differential calculus on quantum groups can be extended by introducing, in analogy with the classical case, inner product operators and Lie derivatives. For the case of $\GL$ we show how this extended calculus induces by coaction a similar extended calculus, covariant under $\GL$, on the quantum plane. In this way, inner product operators and Lie derivatives can be introduced on the plane as well. The situation with other quantum groups and quantum spaces is briefly discussed. Explicit formulas are given for the two dimensional quantum plane.

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