On the variety of two dimensional real associative algebras
classification
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algebraalgebrasassociativedimensionalrealvarietyanalysiscalculate
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This paper consists of a description of the variety of two dimensional associative algebras within the framework of Nonstandard Analysis. By decomposing each algebra in A^2 as sum of a Jordan algebra and a Lie algebra, we calculate the isomorphism classes of two dimensional real associative algebras over the field of real numbers and determine the components and the contractions of the variety.
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