## Hochschild and cyclic homology of finite type algebras.(English)Zbl 0914.16005

For a commutative algebra $$A$$ of finite type the geometry and topology of its primitive ideal spectrum $$\text{Prim}(A)$$ are closely connected with the Hochschild $$HH_\ast(A)$$ and periodic cyclic $$HP_\ast(A)$$ homology groups [see e.g. G. Hochschild, B. Kostant and A. Rosenberg, Trans. Am. Math. Soc. 102, 383-408 (1962; Zbl 0102.27701) and G. Rinehart, ibid. 108, 195-222 (1963; Zbl 0113.26204)]. The authors generalize this to the larger class of finite type algebras. The main result relates $$HP_\ast(A)$$ and the topology of $$\text{Prim}(A)$$ of a finite type algebra $$A$$, showing that the homology groups $$HP_\ast(A)$$ are a good substitute for de Rham cohomology of $$\text{Prim}(A)$$.

### MSC:

 16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 19D55 $$K$$-theory and homology; cyclic homology and cohomology 18G60 Other (co)homology theories (MSC2010) 55N35 Other homology theories in algebraic topology

### Citations:

Zbl 0102.27701; Zbl 0113.26204
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