Algebraic & Geometric Topology

Hochschild homology, Frobenius homomorphism and Mac Lane homology

Teimuraz Pirashvili

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Abstract

We prove that Hi(A,Φ(A))=0, i>0. Here A is a commutative algebra over the prime field Fp of characteristic p>0 and Φ(A) is A considered as a bimodule, where the left multiplication is the usual one, while the right multiplication is given via Frobenius endomorphism and H denotes the Hochschild homology over Fp. This result has implications in Mac Lane homology theory. Among other results, we prove that HML(A,T)=0, provided A is an algebra over a field K of characteristic p>0 and T is a strict homogeneous polynomial functor of degree d with 1<d<Card(K).

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 2 (2007), 1071-1079.

Dates
Received: 14 March 2007
Accepted: 26 March 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796714

Digital Object Identifier
doi:10.2140/agt.2007.7.1071

Mathematical Reviews number (MathSciNet)
MR2336249

Zentralblatt MATH identifier
1137.19001

Subjects
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

Keywords
Hochschild Homology Mac Lane homology

Citation

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


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