伪微分算子模的子代数的等价类
Equivalence classes of subquotients of pseudodifferential operator modules
摘要：
考虑直线上张量密度模之间的伪微分算子空间作为直线上向量场的李代数的模。我们计算这些模块的各种subconquerents的等价类。对于任何给定的Jordan-Holder合成列，都存在一个2参数的子元族.在长度为5的子代数的临界情况下，每个非共振2参数族内的等价类由一束二次曲线与一束三次曲线的交点指定。在长度为4的共振子项具有自对偶合成列的情况下，以及长度为3和4的缺子项的情况下，等价性由单束二次曲线指定。长度超过7的非共振子项不允许非明显的等价。长度为6和7的案件尚未解决。
英文摘要：
Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There is a 2-parameter family of subquotients with any given Jordan-Holder composition series. In the critical case of subquotients of length 5, the equivalence classes within each non-resonant 2-parameter family are specified by the intersections of a pencil of conics with a pencil of cubics. In the case of resonant subquotients of length 4 with self-dual composition series, as well as of lacunary subquotients of lengths 3 and 4, equivalence is specified by a single pencil of conics. Non-resonant subquotients of length exceeding 7 admit no non-obvious equivalences. The cases of lengths 6 and 7 are unresolved.
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