Volume 7, issue 2 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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