Algebra environments provide requisites for studying objects of interest in operator algebra theory, group representation theory, spin geometry, Clifford analysis, and several variable operator theory. The concept is analyzed by developing an algebraic geometry approach. Specific algebraic sets, called structure manifolds of algebra environments, and their Zariski tangent spaces are introduced and described by using as critical tools derivations on algebras. Structure manifolds of tensor environments in particular yield spaces of algebra homomorphisms. Consequently, such spaces could be investigated as algebraic manifolds. Related issues include characterizations of their Zariski tangent spaces and of derivations that preserve algebra homomorphisms.

中文翻译：

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代数环境 II.代数同态和推导

代数环境为研究算子代数理论、群表示理论、自旋几何、Clifford 分析和多变量算子理论中感兴趣的对象提供了必要条件。通过开发代数几何方法来分析该概念。通过使用代数的关键工具推导来介绍和描述特定的代数集，称为代数环境的结构流形及其 Zariski 切线空间。张量环境的结构流形特别产生代数同态空间。因此，这样的空间可以作为代数流形来研究。相关问题包括其 Zariski 切线空间的表征以及保留代数同态的推导。