Aperiodic Virasoro algebra (Q2738098)

Using a special aperiodic set, \(\sigma(\Omega)\), instead of integers as an index set, the author defines the aperiodic analogue for the Witt and Virasoro algebras. In the case \(\Omega=[0,1]\) it is proved that the aperiodic Virasoro algebra is the universal central extension of the corresponding aperiodic Witt algebra. In the same case an analogue of the highest weight representations is constructed and studied, in particular, a conjecture for Kac determinant is formulated. In the last part of the paper the author determines the regions of unitarity, corresponding to the case of positive semidefinite Kac determinant. In three appendices the author explains the central extension formalism for general acceptance windows; presents several formulae for singular vectors in the highest weight modules on the first eight levels and gives some details for the determinant formula.