On the homology of Poisson algebra of odd variables (Q1094527)

The traditional algebraic K-theory is based on the group GL(\(\infty)\). On the category of supercommutative superalgebras over a field of zero characteristic, there are two analogs of this group: GL(\(\infty,\infty)\) and Q(\(\infty)\). The corresponding two K-theories seem to be parts of different parity of a larger ``super K-theory''. Moreover, there is another group closely related to both GL and Q: the group of canonical transformations in mechanics with odd variables. This group can be regarded as a ``classical'' version of ``quantum'' GL and Q. Its homology is related with differential forms on the superalgebra, additive K-theory and cyclic homology.