In the first part of the paper we describe \(\varphi\)-derivations of the incidence algebra I(X, K) of a locally finite poset X over a field K, where \(\varphi\) is an arbitrary automorphism of I(X, K). We show that they admit decompositions similar to that of usual derivations of I(X, K). In particular, the quotient of the space of \(\varphi\)-derivations of I(X, K) by the subspace of inner \(\varphi\)-derivations of I(X, K) is isomorphic to the first group of certain cohomology of X, which is developed in the second part of the paper.

中文翻译：

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关联代数的偏导数

在本文的第一部分中，我们描述了\(\varphi\) -域K上局部有限偏序集X的关联代数I ( X ,  K ) 的推导，其中\(\varphi\)是以下任意自同构我（X，  K）。我们证明它们允许类似于I ( X ,  K ) 的通常推导的分解。特别是，I ( X ,  K )的导数的空间除以I ( X ,  K )的内导数的子空间的商与第一组同构X的某些上同调，这是在本文的第二部分中展开的。