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We show that the universal associative envelope of the simple anti-Jordan triple system of all ( is even, ) matrices over an algebraically closed field of characteristic 0 is finite-dimensional. The monomial basis and the center of the universal envelope are determined. The explicit decomposition of the universal envelope into matrix algebras is given. The classification of finite-dimensional irreducible representations of an anti-Jordan triple system is obtained. The semi-simplicity of the universal envelope is shown. We also show that the universal associative envelope of the simple polarized anti-Jordan triple system of matrices is infinite-dimensional. [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of free objects in the variety of Steiner loops and of the combinatorial structures behind them, focusing on their automorphism groups. We prove that all automorphisms are tame and the automorphism group is not finitely generated if the loop is more than 3-generated. For the free Steiner loop with three generators we describe the generator elements of the automorphism group and some relations between them. [ABSTRACT FROM AUTHOR]