Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 7, Number 2 (2007), 1071-1079.
Hochschild homology, Frobenius homomorphism and Mac Lane homology
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 .
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1071-1079.
Received: 14 March 2007
Accepted: 26 March 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
Secondary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60] 55U10: Simplicial sets and complexes
Pirashvili, Teimuraz. Hochschild homology, Frobenius homomorphism and Mac Lane homology. Algebr. Geom. Topol. 7 (2007), no. 2, 1071--1079. doi:10.2140/agt.2007.7.1071. https://projecteuclid.org/euclid.agt/1513796714