Preprint
Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
A. I. Molev and E. Ragoucy
Abstract
We construct an action of the braid group B_N on the twisted
quantized enveloping algebra U'_q(o_N) where the elements of B_N
act as automorphisms. In the classical limit q > 1 we
recover the action of B_N on the polynomial functions on the
space of upper triangular matrices with ones on the diagonal.
The action preserves the Poisson bracket on the space of
polynomials which was introduced by Nelson and Regge in their
study of quantum gravity and rediscovered in the mathematical
literature. Furthermore, we construct a Poisson bracket on the
space of polynomials associated with another twisted quantized
enveloping algebra U'_q(sp_{2n}). We use the Casimir elements of
both twisted quantized enveloping algebras to reproduce some
wellknown and construct some new polynomial invariants of the
corresponding Poisson algebras.
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