Volume 7, issue 2 (2007)

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Hochschild homology, Frobenius homomorphism and Mac Lane homology

Teimuraz Pirashvili

Algebraic & Geometric Topology 7 (2007) 1071–1079

arXiv: math.KT/0703376

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).

Keywords
Hochschild Homology, Mac Lane homology
Mathematical Subject Classification 2000
Primary: 55P43, 16E40
Secondary: 19D55, 55U10
References
Publication
Received: 14 March 2007
Accepted: 26 March 2007
Published: 2 August 2007
Authors
Teimuraz Pirashvili
Department of Mathematics
University of Leicester
Leicester
LE1 7RH
UK