From Leibniz homology to cyclic homology
Given an algebra \(A\), the author constructs a natural homomorphism \(HL_{\ast+1}(A)\to HH_\ast(A)\) from Leibniz to Hochschild homology. If \(f: A\to B\) is a homorphism of algebras, the relative Leibniz homology \(HL_\ast(gl(f))\) is defined and a natural homomorphism \(HL_{\ast+1}(gl(f))\to HC_\ast(F)\) to relative cyclic homology is studied. Thus, a relation between Leibnitz homology and K-theory via the result of \textit{T. G. Goodwillie} [Ann. Math., II. Ser. 124, 347--402 (1986; Zbl 0627.18004)] has been offered.
scientific article; zbMATH DE number 1925077