A Künneth formula for the cyclic cohomology of \(\mathbb Z/2\)-graded algebras (Q1071854)

The author extends A. Connes' cyclic (co)homology groups to superalgebras (i.e. \(\mathbb Z/2\)-graded algebras). He derives Künneth formulae for the cyclic cohomology of the (skew) tensor product of superalgebras and gives two applications. The first one which is of interest to physicists is the computation of the cyclic cohomology of Clifford and Grassmann algebras. The second one deals with the Lie algebra \(gl(A)=\varinjlim_n gl_n(A)\) of finite matrices with coefficients in an arbitrary associative algebra \(A\) over a field of characteristic zero: we determine \(H_*(gl(A))\oplus_{n>0}S^n gl(A))\) in terms of the Hochschild homology of \(A\) (here \(S^n gl(A)\) stands for the \(n\)-th symmetric power of the adjoint representation).