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On free field realization of the twisted Heisenberg-Virasoro and W(2,2) algebras

We present a free field realization of the Heisenberg-Virasoro vertex- operator algebra HVir and its impact on representation theory of the twisted Heisenberg-Virasoro Lie algebra at level 0. Furthermore, we will see that W(2, 2) vertex operator algebra embeds in HVir and discuss W(2, 2)–structure of irreducible highest weight HVir–modules. This is a joint work with Dražen Adamović.

vertex algebras, Heisenberg-Virasoro algebra, fusion rules

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