We develop a theory of boundary functions for ideals in trivially analyticsubalgebras of simple AF C*-algebras with an injective 0-cocycle, a class whichincludes all full nest algebras. Boundary functions are maps from the spectrumof the diagonal of the analytic subalgebra to itself. The relation betweenboundary functions and ideal sets is explored and a description is given ofmeet and join irreducible boundary functions.
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机译：我们开发了一个简单的AF C *代数的一般分析微分代数的理想理想的边界函数理论，该代数具有可注射的0-cocycle，该类包括所有完整的嵌套代数。边界函数是从解析子代数的对角线光谱到其自身的映射。探索了边界函数与理想集之间的关系，并对满足和不可约边界函数进行了描述。
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