Dimension Formulas for the Free Nonassociative Algebra |
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| Authors: | Murray R Bremner Irvin R Hentzel Luiz A Peresi |
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| Institution: | 1. Research Unit in Algebra and Logic , University of Saskatchewan , Saskatoon, SK, Canada bremner@math.usask.ca;3. Department of Mathematics , Iowa State University , Ames, Iowa, USA;4. Instituto de Matemática e Estatística , Universidade de S?o Paulo , S?o Paulo, Brazil |
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| Abstract: | The free nonassociative algebra has two subspaces which are closed under both the commutator and the associator: the Akivis elements and the primitive elements. Every Akivis element is primitive, but there are primitive elements which are not Akivis. Using a theorem of Shestakov, we give a recursive formula for the dimension of the Akivis elements. Using a theorem of Shestakov and Umirbaev, we prove a closed formula for the dimension of the primitive elements. These results generalize the Witt dimension formula for the Lie elements in the free associative algebra. |
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| Keywords: | Akivis algebras Free algebras Primitive elements Witt dimension formula |
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