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2007 Hochschild homology, Frobenius homomorphism and Mac Lane homology
Teimuraz Pirashvili
Algebr. Geom. Topol. 7(2): 1071-1079 (2007). DOI: 10.2140/agt.2007.7.1071

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).

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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

Information

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

zbMATH: 1137.19001
MathSciNet: MR2336249
Digital Object Identifier: 10.2140/agt.2007.7.1071

Subjects:
Primary: 16E40, 55P43
Secondary: 19D55, 55U10

Rights: Copyright © 2007 Mathematical Sciences Publishers

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