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Do Ngoc Diep

Publications and source records attributed to Do Ngoc Diep.

33 records · Page 2Linked to original sources
arXiv2003

K-Theory and peiodic cyclic homology of some noncompact quantum algebras

We prove in this paper that the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of connected and simply connected Lie group, are isomorphic to the periodic cyclic homology of the quantized algebras of functions on coadjoint orbits of compact maximal subgroups, without localization. Some noncompact quantum groups and algebras were constructed and their irreducible representations were classified in recent works of Do Ngoc Diep and Nguyen Viet Hai, and Do Duc Hanh by using deformation quantization. In this paper we compute their K-groups, periodic cyclic homology groups and their Chern characters.

math.QA↗
arXiv2002

Riemann-Roch Theorem and Index Theorem in Non-commutative Geometry

In this lecture we review apprearance of the Riemann-Roch Theorem in classical function theory, Algebraic topology, in theory of pseudo-differential operators and finally in noncommutative geometry. We show also it usefulness in many problem of quantization and harmonic analysis on Lie groups.

math.OA↗
arXiv2000

Quantum Strata of Coadjoint Orbits

In this paper we construct quantum analogs of strata of coadjoint orbits and describe their representations. This kind objects play an important role in describing quantum groups as repeated extensions of quantum strata.

math.QA↗
arXiv2000

A Survey of Noncommutative Chern Characters

We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their commutative counterparts. This survey can be considered as the second part of the previous survey (J. of Lie Theory vol. 3 (1993), 149-176.

math.QA↗
arXiv1999

Quantum Co-Adjoint Orbits of the Group of Affine Transformations of the Complex Straight Line

We construct start-products on the co-adjoint orbit of Lie group $\Aff({\bf C})$ of affine transformations of the complex straight line and apply them to obtain the irreducible unitary representations of this group. These results show effectiveness of the Fedosov quantization even for groups which are neither nilpotent nor exponential. Together with the result for the group $\Aff({\bf R})$ in math.QA/9905002, we have thus a description of quantum $\bar{MD}$ co-adjoint orbits.

math.QA↗
arXiv1999

Quantum Half-Planes via Deformation Quantization

We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operator $\hat{\ell}_Z$, we show that the resulting representations exhausted all the irreducible representations of this groups.

math.QA↗
arXiv1999

Compact quantum group C^*-algebras as Hopf algebras with approximate unit

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L_2 and C^*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra.

math.QA↗
arXiv1998

Discrete Series for Loop Groups.I. An algebraic Realization of Standard Modules

In this paper we consider the category $C (\tilde k, \tilde H)$ of the $(\tilde k, \tilde H)$-modules, including all the Verma modules, where $k$ is some compact Lie algebra and H some Cartan subgroup, $\tilde k$ and $\tilde H$ are the corresponding affine Lie algebra and the affine Cartan group, respectively. To this category we apply the Zuckerman functor and its derivatives. By using the determinant bundle structure, we prove the natural duality of the Zuckerman derived functors, and deduce a Borel-Weil-Bott type theorem on decomposition of the nilpotent part cohomology.

math.RT↗
arXiv1998

A Geometric Realization of Degenerate Principal Series Representations of Symplectic Groups

The multidimensional quantization procedure, proposed by the first author and its modifications (reduction to radicals and lifting on U(1)-coverings) give us a almost universal theoretical tools to find irreducible representations of Lie groups. By using this method and the root theory, we realize in this paper the representations of the degenerate principal series of symplectic groups.

math.RT↗
arXiv1998

On the Structure of Lie Group C*-Algebras and Compact Quantum Groups

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative de Rham currents and the noncommutative Chern characters, and their computation for C*-algebras of compact Lie groups and compact quantum groups.

math.KT↗
arXiv1998

Non-Commutative Geometry Methods for Group C*-Algebras

This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example of description of the structure of C*-algebras of the group of affine transformations of the real straight line, continued then for special classes of solvable and nilpotent Lie groups. In the second advanced part, we introduced the main tools of the theory. In particular, the conception of multidimensional geometric quantization and the index of group C*-algebras were created and developed.

math.KT↗
arXiv1998

Jeffrey-Kirwan-Witten Localization Formula for Reductions at Regular Co-adjoint Orbits

For Marsden-Weinstein reductions at the point 0 in the vector space dual to the Lie algebra, the well-known Jeffrey-Kirwan-Witten localization formula was proven and lastly modified by M. Vergne. We prove in this paper the same kind formula for the reductions at regular coadjoint orbits by using the universal orbital formula of characters.

math.SG↗
arXiv1998

Non-Commutative Chern Characters of Compact Lie Group C*-Algebras

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology of compact Lie group C*-algebras, define Chern characters between them and show that the Chern characters in both topological and algebraic cases are isomorphisms.

math.KT↗
arXiv1998

Non-Commutative Chern Characters of Compact Quantum Groups

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology for compact quantum groups, define Chern characters between them and show that the Chern characters in both topological and algebraic cases are isomorphisms modulo torsion. The case of compact Lie group C*-algebras was treated in Non-Commutative Chern characters of compact Lie groups C*-algebras, 0257 , a revised version of which was accepted for publication in K-Theory.

math.QA↗