Abstract
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) Hoft 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.
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