TAILIEUCHUNG - Báo cáo " Non-commutative chern characters of the $C^*-$algebras of the sphers "

We propose in this paper the construcion of non-commutative Chern characters of the $C^*-$algebras of spheres and quantum spheres. The final computation gives us clear relation with the ordinary $\mathbb Z/(2)-$graded Chern chracters of torsion or their normalizers. | VNU Journal of Science Mathematics - Physics 25 2009 249-259 Non-commutative chern characters of the Ơ -algebras of the sphcrs Nguyen Quoc Tho Department of Mathematics Vĩnh University 12 Le Duan Vĩnh city Vietnam Received 8 September 2009 Abstract. We propose in this paper the construcion of non-commutative Chern characters of the c algebras of spheres and quantum spheres. The final computation gives US clear relation with the ordinary z 2 graded Chern chracters of torsion or their normalizers. Keyworks Characters of the c algebras. 1. Introduction For compact Lie groups the Chem character ch K G Q were constructed. In 4 - 5 we computed the non-commutative Chem characters of compact Lie goup c algebras and of compact quantum groups which are also homomorphisms from quantum K groups into entire current periodic cyclic homology of group c algebras resp. of c algebra quantum groups chc H C G resp. chc We obtained also the corresponding algebraic vesion chaig K C G which coincides with the Fedosov-Cuntz- Quillen formula for Chem characters 5 . When A C G we first computed the K groups of C G and the HE C GỴ . Thereafterwe computed the Chem character chc K C G HE C G as an isomorphism modulo torsions. Using the results from 4 - 5 in this paper we compute the non-commutative Chem characters chc K A HE A for two cases A C SnỴ the c algebra of spheres and A c sn the c algebras of quantum spheres. For compact groups G o n 1 the Chem character ch K sn Q HRR Sn Q of the sphere sn o n l o n is an isomorphism se 15 . In the paper we describe two Chem character homomorphisms ch j K C Sn HE C Sn f and ch j K C SnỴ HE C jSnỴ . E-mail thonguyenquoc@ 249 250 . Bang et al. VNU Journal of Science Mathematics - Physics 25 2009 249-259 Finally we show that there is a commutative diagram K C Sny EtE C Sn K C A -TJ HEfc xTn K AÍTn HE drỤ ítJ Similarly for A c n we have an analogous commutative diagram with w X s1 of place of w X sn from which we deduce that chc is an .

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