, Volume 22, Issue 3, pp 1285-1289

Complexity of “wild” matrix problems and of isomorphism of algebras and graphs

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It is shown that isomorphism of semisimple algebras over an algebraically closed field is recognized in polynomial time. The polynomial equivalence of isomorphism of graphs and isomorphism of algebras (over an algebraically closed field) with zero square of the radical and commutative quotient modulo the radical is proved. A series of problems about the complexity of matrix problems and isomorphism of algebras are posed.

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 105, pp. 10–16, 1981.