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Fundamental Solution of the Heat and Schrödinger Equations with Point Interaction
Abstract We find explicit formulae for the fundamental solution for the heat and time dependent Schrodinger equations with point interaction in dimension n ≤ 3. We discuss in detail the small timeExpand
Dirac operator on the standard Podles quantum sphere
Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, realityExpand
Noncommutative Borsuk-Ulam-type conjectures
Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if $H$ is the C*-algebra of a compact quantum groupExpand
Some Properties of Non-linear $\sigma$-Models in Noncommutative Geometry
We introduce non-linear $\sigma$-models in the framework of noncommutative geometry with special emphasis on models defined on the noncommutative torus. We choose as target spaces the two point spaceExpand
Dirac operators on all Podles quantum spheres
We construct spectral triples on all Podles quantum spheres S 2 qt . These noncom- mutative geometries are equivariant for a left action of Uq(su(2)) and are regular, even and of metric dimension 2.Expand
Symmetries of Schrödinger Operator with Point Interactions
The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, thoseExpand
A(SLq(2)) at Roots of Unity is a Free Module over A(SL(2))
It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SLq(2)) is a free module of finite rank over the coordinate ring of the classical group SL(2). An explicit set ofExpand
The Dirac Operator on SUq(2)
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 theExpand
Curved noncommutative torus and Gauss–Bonnet
We study perturbations of the flat geometry of the noncommutative two-dimensional torus Tθ2 (with irrational θ). They are described by spectral triples (Aθ,H,D), with the Dirac operator D, which is aExpand
Spinors and diffeomorphisms
We discuss the action of diffeomorphisms on spinors on an oriented manifoldM. To do this, we first describe the action of the diffeomorphism groupD(M) on the set Π =H1 (M,Z2) of inequivalent spinExpand