Hochschild (co)homology of exterior algebras using algebraic Morse theory

摘要

In 1, the authors computed the additive and multiplicative structure of HH* (A; A), where A is the n-th exterior algebra over a field. In this paper, we derive all their results using a different method (AMT) as well as calculate he additive structure of HHk(A;A) and HHk(A; A) over Z. We provide concise presentations of algebras HH* (A; A) and HH* (A; A) as well as determine heir generators in the Hochschild complex. Finally, we compute an explicit free resolution (spanned by multisets) of the A(e)-module A and describe the homotopy equivalence to its bar resolution.