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Efficient Decomposition of Associative Algebras over Finite Fields
2000
Journal of symbolic computation
We present new, efficient algorithms for some fundamental computations with finitedimensional (but not necessarily commutative) associative algebras over finite fields. For a semisimple algebra A we show how to compute a complete Wedderburn decomposition of A as a direct sum of simple algebras, an isomorphism between each simple component and a full matrix algebra, and a basis for the centre of A. If A is given by a generating set of matrices in F m×m , then our algorithm requires about O(m 3 )
doi:10.1006/jsco.1999.0308
fatcat:myr6prcksrge3fufgqbxa6rlsa