Algebras associated to the Young-Fibonacci lattice

Author:
Soichi Okada

Journal:
Trans. Amer. Math. Soc. **346** (1994), 549-568

MSC:
Primary 05E99; Secondary 06B99

MathSciNet review:
1273538

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Abstract: The algebra generated by subject to the defining relations is shown to be a semisimple algebra of dimension if the parameters are generic. We also prove that the Bratteli diagram of the tower of these algebras is the Hasse diagram of the Young-Fibonacci lattice, which is an interesting example, as well as Young's lattice, of a differential poset introduced by . Stanley. A Young-Fibonacci analogue of the ring of symmetric functions is given and studied.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1994-1273538-7

Keywords:
Young-Fibonacci lattice,
differential poset,
Bratteli diagram

Article copyright:
© Copyright 1994
American Mathematical Society