On Evolution Algebras
J. M. CasasDepartment of Applied Mathematics, E.U.I.T. Forestal, Pontevedra, University of Vigo, 36005, SpainM. LadraDepartment of Algebra, University of Santiago de Compostela, 15782, SpainB. A. OmirovU. A. Rozikov
2014en
ABI
Abstract
The structural constants of an evolution algebra are given by a quadratic matrix. In this work we establish an equivalence between nil, right nilpotent evolution algebras and evolution algebras defined by upper triangular matrices. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix, we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.
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Cited by 20 references