Associative and Jordan shift algebras

Authors:
Ottmar Loos and Erhard Neher

Journal:
Proc. Amer. Math. Soc. **120** (1994), 27-36

MSC:
Primary 17C65; Secondary 16S99

MathSciNet review:
1158003

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Abstract: Let be the shift algebra, i.e., the associative algebra presented by generators and the relation . As N. Jacobson showed, contains an infinite family of matrix units. In this paper, we describe the Jordan algebra and its unital special universal envelope by generators and relations. Moreover, we give a presentation for the Jordan triple system defined on by where is the involution on with . As a consequence, we prove the existence of an infinite rectangular grid in a Jordan triple system containing tripotents and with and .

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1158003-5

Article copyright:
© Copyright 1994
American Mathematical Society