KOSZUL RESOLUTIONS
KOSZUL RESOLUTIONS
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DOI：
10.1090/s0002-9947-1970-0265437-8
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通讯作者：
Stewart B. Priddyh
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作者：
Stewart B. Priddyh
.本文对一类增广代数，包括Steenrod代数和泛包络代数，构造了经典的Koszul分解，推广了经典的Koszul分解。对于每个这样的代数A，描述一个显式微分代数K*（A），使得（1）K*（A）是cobar复形的小商代数，（2）K*（A）的同调是上同调代数H*（A）。恢复了特征为2的限制李代数的May分解，并给出了Kan等人关于Steenrod代数的分解的一个简单推导.
. Resolutions, which generalize the classical Koszul resolutions, are constructed for a large class of augmented algebras including the Steenrod algebra and the universal enveloping algebras. For each such algebra A, an explicit differential algebra K*(A) is described such that (1) K*(A) is a small quotient algebra of the cobar complex and (2) the homology of K*(A) is the cohomology algebra H*(A). The resolution of May for restricted Lie algebras in characteristic 2 is retrieved and a simple derivation of the resolution of Kan et al. of the Steenrod algebra is given.