Sugawara construction and the q-deformation of Virasoro (super)algebra

The q-deformed Virasoro algebra is obtained using the bosonic annihilation and creation operators of the q-deformed infinite Heisenberg algebra H(∞)q, which has the Hopf structure. The generators of the q-deformed Virasoro algebra are expressed as a Sugawara construction in terms of normal ordered binomials in these annihilation and creation operators and become double indexed as the reminiscence of a degeneracy removal. The obtained q-deformed Virasoro algebra with central extension reduces to the standard one in the non-deformed limit and in special representations (but not in general) possesses a simple (cocommutative) Hopf structure [not related to the one in H(∞)q]. The fermionic annihilation and creation operators corresponding to the q-deformed infinite Heisenberg superalgebra s-H(∞)q necessary for a similar construction of the q-deformed Virasoro superalgebra are presented. (orig.)