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In this paper we study algebraic structures of the classes of the $L_2$analytic Fourier-Feynman transforms on Wiener space. To do this we firstdevelop several rotation properties of the generalized Wiener integralassociated with Gaussian processes. We then proceed to analyze the $L_2$analytic Fourier-Feynman transforms associated with Gaussian processes. Ourresults show that these $L_2$ analytic Fourier--Feynman transforms are actuallylinear operator isomorphisms from a Hilbert space into itself. We finallyinvestigate the algebraic structures of these classes of the transforms onWiener space, and show that they indeed are group isomorphic.

Algebraic structure of the $L_2$ analytic Fourier-Feynman transform associated with Gaussian processes on Wiener space