Semiinfinite Cohomology of Tate Lie Algebras

摘要

This note is a natural extension of the final part in (Ar) where a naturalhomological construction for a graded lie algebra semiinfinite cohomology and a natural explanation for the phenomenon of the critical cocycle was found. Here the authors propose a variant of the construction that works in the Tate Lie algebra case. Note that the standard complex for the computation of the Tate Lie algebra semiinfinite cohomology was written down by Beilinson and Drinfeld in (BD) and probably by some physicists. Still the construction was rather an indirect one and was not formulated in terms similar to the ones in (Ar). In this note the authors spell out the construction of the complex in terms of some kind of quadratic-linear Koszul duality rather than Conformal Field Theory.