The tangential Cauchy–Fueter complex on the quaternionic Heisenberg group
The tangential Cauchy–Fueter complex on the quaternionic Heisenberg group
复制标题
DOI：
10.1016/j.geomphys.2010.10.006
复制
发表时间：
2011
影响因子：
1.5
通讯作者：
Wei Wang
中科院分区：
文献类型：
--
作者：
Wei Wang
四元空间上的 Cauchy-Fueter 算子 H 引入域边界上的切向 Cauchy-Fueter 算子。四元数海森堡群是边界的标准模型。通过使用与 Sp(2N,C) 齐次空间的双纤维化相关的彭罗斯变换，我们在四元数海森堡群（切向 k-Cauchy-Fueter 复合体）上构造了一个精确序列，求解了切向 k-Cauchy-Fueter 算子 Q0(k)。 Q0(1) 是切向 Cauchy-Fueter 算子。该复形给出了非齐次切向 k-Cauchy-Fueter 方程 Q0(k)u=f 可解的相容条件。该复形中的算子是四元数海森堡群上的左不变微分算子。这是多复变量理论中海森堡群上 ∂¯b 复形的四元数版本。
The Cauchy–Fueter operator on the quaternionic space Hninduces the tangential Cauchy–Fueter operator on the boundary of a domain. The quaternionic Heisenberg group is a standard model of the boundaries. By using the Penrose transformation associated to a double fibration of homogeneous spaces of Sp(2N,C), we construct an exact sequence on the quaternionic Heisenberg group, the tangential k-Cauchy–Fueter complex, resolving the tangential k-Cauchy–Fueter operator Q0(k). Q0(1)is the tangential Cauchy–Fueter operator. The complex gives the compatible conditions under which the non-homogeneous tangential k-Cauchy–Fueter equations Q0(k)u=f are solvable. The operators in this complex are left invariant differential operators on the quaternionic Heisenberg group. This is a quaternionic version of ∂¯b-complex on the Heisenberg group in the theory of several complex variables.