NDLI: Nonassociative polynomial identities, Young tableaux and computers

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Nonassociative polynomial identities, Young tableaux and computers

Content Provider	ACM Digital Library
Author	Cattaneo, G. M. Piacentini Pittaluga, M.
Abstract	One of the problems which arises in nonassociative algebra is to find an efficient way to handle and to classify polynomial identities, because of the number of summands which appear in their expression. In this paper we show that the results in the literature on enumeration of minimal identities of particular degrees are simply particular cases of the well understood theory of Young tableaux and the representations of the symmetric groups, and as such can be generated mechanically by a computer. By applying a method introduced by Regev in the study of (associative) P.I. algebras, we show that one may classify directly from the standard tableaux all (associative or nonassociative) minimal identities of a given degree based on any set of forms of association. This method has the advantage, with respect to the similar technique used repeatedly in papers by Hentzel and Piacentini (for an explanation of the technique, see for example Hentzel [3],[4], and Hentzel-Piacentini [5]), that it may be easily implemented on a computer to solve the problem of classifying identities, with very little computing time; this allows one to handle identities of high degree, which was almost impossible until now. The implementation of the algorithm has been performed on a Micro VAX of our Department, using Common Lisp.
Starting Page	17
Ending Page	26
Page Count	10
File Format	PDF
ISSN	01635824
DOI	10.1145/43876.43878
Journal	ACM SIGSAM Bulletin (SIGS)
Volume Number	22
Issue Number	2
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1998-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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