Discrete, q-difference deformations of associative algebras and integrable systems

Details Discrete, q-difference deformations of associative algebras and integrable systems Discrete, q-difference deformations of associative algebras and integrable systems

2008-09-11

arxiv.org/abs/0809.1938v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Talk given at the workshop SIDE8, June 22-28, 2008, Sainte-Adele, Canada

Scientific paper

Discrete and q-difference deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by a central system of discrete or q-difference equations which in particular cases represent discrete and q-difference versions of the oriented associativity equation. It is demonstrated also that the celebrated Hirota-Miwa bilinear equation for the AKP and BKP hierarchies describes discrete deformations of certain finite-dimensional algebras.

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