Lie algebra generated by logarithm of differentiation and logarithm
نویسنده
چکیده
Let log ( d dx ) be the generator of the1-parameter group { d dxa |a ∈ R} of fractional order differentiations acting on the space of operators of Mikusinski ([5]). The Lie algebra glog generated by log ( d dx ) and log x is a deformation and can be regarded as the logarithm of Heisenberg Lie algebra. We show glog is isomorphic to the Lie algebra generated by d ds log(Γ(1 + s)) and d ds . Hence as a module, glog is isomorphic to the module generated by d ds and polygamma functions. Structure of the group generated by 1-parameter groups { d dxa |a ∈ R} and {xa|a ∈ R}, is also determined. M.S.C. 2010: 17B65, 26A33, 44A15, 81R10.
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