Vladimir L. Popov: Generic algebras: rational parametrization and normal forms


Submission: 2014, Nov 27

For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Generic finite dimensional (not necessarily associative) k-algebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over k rational functions in the structure constants. (2) There exists an "algebraic normal form", to which the set of structure constants of every such algebra can be uniquely transformed by means of passing to its new basis.

2010 Mathematics Subject Classification: 17-XX, 20Gxx, 14M20, 13A50, 14R20

Keywords and Phrases: finite dimensional algebra, rationality, normal form

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