On Evolution Algebras  

作　　者：J.M. Casas M. Ladra B.A. Omirov U.A. Rozikov 

机构地区：[1]Department of Applied Mathematics, E. U.I.T. Forestal, Pontevedra University of Vigo, 36005, Spain [2]Department of Algebra, University of Santiago de Compostela, 15782, Spain [3]Institute of Mathematics, Tashkent, 100125, Uzbekistan

出　　处：《Algebra Colloquium》2014年第2期331-342,共12页代数集刊（英文版）

摘　　要：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.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.

关 键 词：evolution algebra nil algebra right nilpotent algebra group of endomor-phisms classification 

分 类 号：O151.21[理学—数学] TM131[理学—基础数学]