113 research outputs found
A Note on Dirac Operators on the Quantum Punctured Disk
We study quantum analogs of the Dirac type operator
on the punctured disk, subject to
the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the
quantum operator and show that it is bounded outside of the zero mode
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
The goal of this paper is to introduce a class of operators, which we call
quantum Dirac type operators on a noncommutative sphere, by a gluing
construction from copies of noncommutative disks, subject to an appropriate
local boundary condition. We show that the resulting operators have compact
resolvents, and so they are elliptic operators
A -Adic Spectral Triple
We construct a spectral triple for the C-algebra of continuous functions
on the space of -adic integers by using a rooted tree obtained from
coarse-grained approximation of the space, and the forward derivative on the
tree. Additionally, we verify that our spectral triple satisfies the properties
of a compact spectral metric space, and we show that the metric on the space of
-adic integers induced by the spectral triple is equivalent to the usual
-adic metric
Global boundary conditions for a Dirac operator on the solid torus
We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary
conditions on the solid torus and show that the corresponding boundary value
problem is elliptic, in the sense that the Dirac operator has a compact
parametrix
Action of Complex Symplectic Matrices on the Siegel Upper Half Space
The Siegel upper half space, Sn, the space of complex symmetric matrices, Z with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, ΦS, where S is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which ΦS(Z) is well defined. We also consider Sn and Sn as metric spaces and discuss distance properties of the map ΦS from Sn to Sn and Sn respectively
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