Geodesic
Hochschild homology, Frobenius homomorphism and Mac Lane homology
Pirashvili, Teimuraz1
1Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1071-1079
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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).

DOI : 10.2140/agt.2007.7.1071
Keywords: Hochschild Homology, Mac Lane homology

Pirashvili, Teimuraz  1

1 Department of Mathematics, University of Leicester, Leicester, LE1 7RH, UK 
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Pirashvili, Teimuraz. Hochschild homology, Frobenius homomorphism and Mac Lane homology. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 1071-1079. doi: 10.2140/agt.2007.7.1071

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