The Cartan Invariant Matrix Of The Finite Chevalley Group SL(3,13) Of Type A₂

At the end of the 19th century there was a growing interest in the possible "hypercomplex sys-tem" over such fields as R and C, what we would now call associative algebras. E. Cartan studied such systems in some generality and associated to them with numerical invariants, which are called Cartan invariants now. Since Chevalley showed in 1955 how to construct simple groups of Lie type, computation of Cartan invariants has become one of the important aspects of the modular represen-tation theory of finite groups of Lie type. The Cartan invariant matrix C= (?)λ,μ∈X1(T) of the finite Chevalley group G(1)= SL(3,13) of type A2 is determined.