In this paper, we study matricial representations of certain finitely presented groups Γ 2 N with N -generators of order-2. As an application, we consider a group algebra A 2 of Γ 2 2 , under our representations. Specifically, we characterize the inverses g −1 of all group elements g in Γ 2 2 , in terms of matrices in the group algebra A 2 . From the study of this characterization, we realize there are close relations between the trace of the radial operator of A 2 , and the Lucas numbers appearing in the Lucas triangle.1991 Mathematics Subject Classification. 05A19, 30E50, 37E99, 44A60.

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