We prove that , . Here is a commutative algebra over the prime field of characteristic and is considered as a bimodule, where the left multiplication is the usual one, while the right multiplication is given via Frobenius endomorphism and denotes the Hochschild homology over . This result has implications in Mac Lane homology theory. Among other results, we prove that , provided is an algebra over a field of characteristic and is a strict homogeneous polynomial functor of degree with .
Teimuraz Pirashvili. "Hochschild homology, Frobenius homomorphism and Mac Lane homology." Algebr. Geom. Topol. 7 (2) 1071 - 1079, 2007. https://doi.org/10.2140/agt.2007.7.1071