The Dirac Operator on SUq(2)
The Dirac Operator on SUq(2)
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SUq(2) 上的狄拉克算子
DOI：
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发表时间：
2004
期刊：
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通讯作者：
J. C. Várilly
中科院分区：
文献类型：
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作者：
L. Dąbrowski;G. Landi;A. Sitarz;W. D. Suijlekom;J. C. Várilly
我们在量子群SUq（2）上构造了一个3+-可和的谱三元组，它关于的左作用和右作用是等变的。由于算子D的谱与三维球面上通常的Dirac算子的谱相同，因此几何与经典情形是等谱的。等变真实的结构J的存在需要在谱几何的公理框架中进行修改，从而仅需要满足任意高阶模无穷小的交换子和一阶性质。
We construct a 3+-summable spectral triple over the quantum group SUq(2) which is equivariant with respect to a left and a right action of The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.