Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications
Keyword(s):
In this paper, we study matricial representations of certain finitely presented groups Γ2Nwith N-generators of order-2. As an application, we consider a group algebra A2 of Γ22; under our representations. Specifically, we characterize the inverses g-1of all group elements g in Γ22; in terms of matrices in the group algebra A2. From the study of this characterization, we realize there are close relations between the trace of the radial operator of A2; and the Lucas numbers appearing in the Lucas triangle. KEYWORDS: Matricial Representation; Group Presentation; Group Algebras; Lucas Numbers; Lucas Triangle; Finitely Presented Group;Group Relations; Free Probability
1974 ◽
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2004 ◽
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2018 ◽
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1974 ◽
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