arXiv subjects

Aderemi O. Kuku

Publications and source records attributed to Aderemi O. Kuku.

4 recordsLinked 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↗

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

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↗