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K-theory — 5 results found.

      
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A Modification of the Effros-Handelman-Shen Theorem with $\mathbb{Z}_2$ actions
C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (3) 2021, pp. 87-102
Bit Na Choi; Andrew J. Dean (Received: 2021/04/08)

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We show that a \(\mathbb{Z}_2\) action on a lattice-ordered dimension group will arise as an inductive limit of \(\mathbb{Z}_2\) actions on simplicial groups. The motivation for this study is the range of invariant problem in Elliott and Su’s classification of AF type \(\mathbb{Z}_2\) actions. We modify the proof of the Effros-Handelman-Shen theorem to include \(\mathbb{Z}_2\) actions.

Nous montrons qu’une action de \(\mathbb{Z}_2\) sur un groupe de dimension ordonné par treillis apparaît comme une limite inductive d’actions de \(\mathbb{Z}_2\) sur des groupes simpliciaux. La motivation de cette étude est le problème de la gamme de l’invariant dans la classification d’Elliott et de Su des actions de \(\mathbb{Z}_2\) de type AF. Nous modifions la preuve du théorème d’Effros-Handelman-Shen pour inclure les actions de \(\mathbb{Z}_2\).

Uniqueness of the Index Map in Banach Algebra K-theory, II
C. R. Math. Rep. Acad. Sci. Canada Vol. 40 (3) 2018, pp. 91-100
George A. Elliott (Received: 2018/09/01, Revised: 2018/09/01)

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It is shown that the index map in the theory of real Banach algebras is unique as a natural transformation, up to an integral multiple, and modulo a (unique) two-torsion “ghost” map arising from the order-two K\(_1\)-group of the Banach algebra \({\mathbb R}\) (of real numbers). (In the earlier paper this was shown for complex Banach algebras, of course without the “ghost” map, but in way—using Bott periodicity to pass to the opposite parity—that is not available for real Banach algebras. The present approach yields a new proof in the complex case.)

On démontre que l’application index dans la K-théorie des algèbres de Banach réelles (ou complexes) est essentiellment unique.

Uniqueness of the Index Map in Banach Algebra K-Theory
C. R. Math. Rep. Acad. Sci. Canada Vol. 36 (2-3) 2014, pp. 93–96
George A. Elliott (Received: 2014/06/18)

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It is shown that the index map in Banach algebra K-theory, as a natural map from the K\(_1\)-group of a quotient of a Banach algebra to the K\(_0\)-group of the corresponding ideal, is unique (up to an integral multiple).

Il est démontré que l’application index dans la K-théorie des algèbres de Banach est unique, dans un sens très naturel.

Torsion in the ${K_0}$-Group of a Recursive Subhomogeneous Algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (4) 2009, pp. 107–114
Sandro Molina-Cabrera (Received: 2009/07/20)

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We show that the \(K_0\)-group of an inductive limit of recursive subhomogeneous algebras with compact metrizable spaces of dimension at most one as local spectra is torsion free. This result implies that the \(K_0\)-group of a unital simple AH algebra which is the inductive limit of recursive subhomogeneous algebras, with compact metrizable spaces of dimension at most one as local spectra, is torsion free. This proves that Li’s reduction theorem for the dimension of the local spectra of unital simple AH algebras cannot be improved, in other words, that the dimension of the local spectra of unital simple AH algebras cannot be further reduced from two to one, even when we use subhomogeneous algebras. This also shows that if a reduction theorem for the dimension of the local spectra of simple inductive limits of recursive subhomogeneous algebras exists, then, after the reduction, the local spectra of the building blocks cannot always be one dimensional.

Nous démontrons que le \(K_0\)-groupe d’une limite inductive des algèbres sous-homogènes récursives, dont les spectres locaux consistent en des espaces compacts métrisables de dimension au plus un, n’a pas de torsion. Ce résultat implique que les \(K_0\)-groupes d’une algèbre AH simple et avec l’unité qui est la limite des algèbres sous-homogènes rećursives, dont les spectres locaux consistent en des espaces compacts métrisables de dimension au plus un, n’a pas de torsion. Cela prouve que le théorème de Li de la réduction pour la dimension des spectres locaux des algèbres AH simples et avec l’unité ne peut pas être améliorée, en d’autres termes, que la dimension des spectres locaux des algèbres AH simples et avec l’unité ne peut pas encore être réduit de deux à un, même quand on utilise des algèbres sous-homogènes. Cela montre aussi que si un théorème de réduction pour la dimension des spectres locaux d’une limite inductive simple des algèbres sous-homogènes récursives existe, alors, après la réduction, les spectres locaux des blocs de construction ne peuvent pas être toujours de dimension un.

On the irrational quartic algebra
C. R. Math. Rep. Acad. Sci. Canada Vol. 21 (3) 1999, pp. 91–96
S.G. Walters (Received: 1998/10/22)

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Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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