Related papers: Morita Theory in Deformation Quantization
We define a notion of equivalence between algebraic dependent type theories which we call Morita equivalence. This notion has a simple syntactic description and an equivalent description in terms of models of the theories. The category of…
This work is the final version of my master thesis. Many, but not all of its key results are already available as a preprint with Chiara Esposito and Stefan Waldmann on arxiv.org under the title "Convergence of the Gutt Star Product", which…
Many interesting C*-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I define…
We consider formal deformations of the Poisson algebra of functions (with singularities) on $T^*M$ which are Laurent polynomials of fibers. Tn the case: $\dim M=1$ ($M=S^1, {\bf R}$), there exists a non-trivial $\star$-product on this…
It seems that Morita invariance is a useful criterion for judging the importance of the classes of ring extensions concerned. Y. Miyashita introduced the notion of Morita equivalence in ring extensions, and he showed that the classes of…
Quantization of classical systems using the star-product of symbols of observables is discussed. In the star-product scheme an analysis of dual structures is performed and a physical interpretation is proposed. At the Lie algebra level…
Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra ({\em full centre}) in the monoidal centre of the monoidal…
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
We consider the Poisson algebra S(M) of smooth functions on T^*M which are fiberwise polynomial. In the case where M is locally projectively (resp. conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.…
We give a Morita equivalence theorem for so-called cyclotomic quotients of affine Hecke algebras of type B and D, in the spirit of a classical result of Dipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the representation…
Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex"…
In this paper the deformation quantization is constructed in the case of scalar fields on Minkowski space-time. We construct the star products at three level concerning fields, Hamiltonian functionals and their underlying structure called…
We classify pointed fusion categories C(G, $\omega$) up to Morita equivalence for 1 < |G| < 32. Among them, the cases |G| = 2 3 , 2 4 and 3 3 are emphasized. Although the equivalence classes of such categories are not distinguished by their…
For a function algebra A we investigate relations between the following three topics: isomorphisms of singly generated A-modules, Morita equivalence bimodules, and `real harmonic functions' with respect to A. We also consider certain groups…
We introduce $C^*$-algebras associated to directed graphs of groups. In particular, we associate a combinatorial $C^*$-algebra to each row-finite directed graph of groups with no sources, and show that this $C^*$-algebra is Morita…
We study formal and non-formal deformation quantizations of a family of manifolds that can be obtained by phase space reduction from $\mathbb{C}^{1+n}$ with the Wick star product in arbitrary signature. Two special cases of such manifolds…
We use recent progress on Chern-Simons gauge theory in three dimensions [18] to give explicit, closed form formulas for the star product on some functions on the affine space ${\mathcal A}(\Sigma)$ of (smooth) connections on the trivialized…
We classify fusion categories which are Morita equivalent to even parts of subfactors with index $3+\sqrt{5} $, and module categories over these fusion categories. For the fusion category $\mathcal{C} $ which is the even part of the…
We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought of as a families version of Donaldson's…