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A Basis for Free Assosymmetric Algebras

✍ Scribed by Irvin Roy Hentzel; David Pokrass Jacobs; Luiz Antonio Peresi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
150 KB
Volume
183
Category
Article
ISSN
0021-8693

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✦ Synopsis

Assosymmetric algebras are nonassociative algebras, where xy z y x yz remains invariant under each permutation of x, y, z. In general, the free nonassociative algebra in a variety is difficult to describe. We show this is not the case for free assosymmetric algebras having characteristic /2, 3. We exhibit a natural basis, describe how basis elements are multiplied and show how arbitrary elements can be expressed relative to this basis.

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