We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group Cq[ SL2], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for q an odd rth root of unity that its eigenvalues are given by q-integers [m]q for m=0,1...,r–1 offset by the constant background curvature. We fully solve the Dirac equation for r=3. 相似文献
After a short introduction, we show how the canonical formalism is constructed in space-time noncommutative theories such
that it allows defining the notion of first-class constraints and analyzing gauge symmetries. We use this formalism to noncommutatively
deform the two-dimensional string gravity (also known as the Witten black hole).
Dedicated to Yu. V. Novozhilov on the occasion of his 80th birthday
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 64–79, July, 2006. 相似文献
Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant quantities. The connection will be enveloping algebra valued in a particular representation of the Lie algebra. This gives rise to additional fields, which couple only weakly via the deformation parameter θ and reduce in the commutative limit to free fields. Consistent field equations that lead to conservation laws are derived and some properties of such theories are discussed. 相似文献
Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, i.e. generalized eigenvalues, to these maps. We show, for the case of Grassmannand Clifford products, that twist maps significantly alter these data reducing degeneracies. Since non group like coproducts give rise to non classical behavior of the algebra of functions, makeing them noncommutative, we hope to be able to learn more about such geometries. A remarkabe thechnicallity is that the coproduct for positive singular values of eigenvectors in A yields directly corresponding eigenvectors in A⊗ A. 相似文献
An -tuple of operators on a Hilbert space is called a -constrained row contraction if and
where is a WOT-closed two-sided ideal of the noncommutative analytic Toeplitz algebra and is defined using the -functional calculus for row contractions.
We show that the constrained characteristic function associated with and is a complete unitary invariant for -constrained completely non-coisometric (c.n.c.) row contractions. We also provide a model for this class of row contractions in terms of the constrained characteristic functions. In particular, we obtain a model theory for -commuting c.n.c. row contractions.
We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of
functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes (BC) quantum statistical mechanical
system and the second on the Habiro ring, where the Habiro functions have, in addition to evaluations at roots of unity, also
full Taylor expansions. Both have compatible endomorphisms actions of the multiplicative semigroup of positive integers. As
a higher dimensional generalization, we consider a crossed product ring obtained using Manin’s multivariable generalizations
of the Habiro functions and an action by endomorphisms of the semigroup of integer matrices with positive determinant. We
then construct a corresponding class of multivariable BC endomotives, which are obtained geometrically from self maps of higher
dimensional algebraic tori, and we discuss some of their quantum statistical mechanical properties. These multivariable BC
endomotives are universal for (torsion free) Λ-rings, compatibly with the Frobenius action. Finally, we discuss briefly how
Habiro’s universal Witten-Reshetikhin-Turaev invariant of integral homology 3-spheres may relate invariants of 3-manifolds
to gadgets over and semigroup actions on homology 3-spheres to endomotives.
The text was submitted by the author in English. 相似文献
The generalized Thirring model with impurity coupling is defined ontwo-dimensional noncommutative space-time, a modified propagator and freeenergy are derived by means of functional integrals method. Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background. 相似文献
This paper completes the classification of Artin-Schelter regular algebras of global dimension three. For algebras generated by elements of degree one this has been achieved by Artin, Schelter, Tate and Van den Bergh. We are therefore concerned with algebras which are not generated in degree one. We show that there exist some exceptional algebras, each of which has geometric data consisting of an elliptic curve together with an automorphism, just as in the case where the algebras are assumed to be generated in degree one.
In particular, we study the elliptic algebras , , and , where , which were first defined in an earlier paper. We omit a set consisting of 11 specified points where the algebras become too degenerate to be regular. Theorem.Let represent , or , where . Then is an Artin-Schelter regular algebra of global dimension three. Moreover, is a Noetherian domain with the same Hilbert series as the (appropriately graded) commutative polynomial ring in three variables.
This, combined with our earlier results, completes the classification.