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Journal articles on the topic 'UHF algebras'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

OHNO, HIROMICHI. "EXTENDABILITY OF GENERALIZED QUANTUM MARKOV CHAINS ON GAUGE INVARIANT C*-ALGEBRAS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 01 (2005): 141–52. http://dx.doi.org/10.1142/s0219025705001901.

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2

Baker, Richard L. "Triangular UHF algebras." Journal of Functional Analysis 91, no. 1 (1990): 182–212. http://dx.doi.org/10.1016/0022-1236(90)90052-m.

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3

Wassermann, Simon. "Subquotients of UHF C*-algebras." Mathematical Proceedings of the Cambridge Philosophical Society 115, no. 3 (1994): 489–500. http://dx.doi.org/10.1017/s030500410007225x.

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Over the last thirty years, the study of C*-algebras has proceeded in a number of directions. On one hand, much effort has been devoted to understanding the structure of particular classes of algebras, such as the approximately finite (AF) algebras. On the other, general structure theorems have been sought. Classes of algebras defined by certain abstract properties have been investigated with a view to obtaining more concrete descriptions of the algebras. One of the earliest results of this type was the theorem of Glimm [13], later extended by Sakai [20] to the inseparable case, characterizing

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4

OHNO, H. "FACTORS GENERATED BY C*-FINITELY CORRELATED STATES." International Journal of Mathematics 18, no. 01 (2007): 27–41. http://dx.doi.org/10.1142/s0129167x07003947.

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We present several equivalent conditions for C*-finitely correlated states defined on the UHF algebras to be factor states and consider the types of factors generated by them. Subfactors generated by generalized quantum Markov chains defined on the gauge-invariant parts of the UHF algebras are also discussed.

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5

Conrad, Joseph F. "Transpositions of UHF algebras." MATHEMATICA SCANDINAVICA 67 (June 1, 1990): 259. http://dx.doi.org/10.7146/math.scand.a-12337.

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6

Hudson, T. D., and E. G. Katsoulis. "Primitive Triangular UHF Algebras." Journal of Functional Analysis 160, no. 1 (1998): 1–27. http://dx.doi.org/10.1006/jfan.1998.3336.

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7

Archbold, R. J., and Alexander Kumjian. "Nuclear subalgebras of UHF C*-algebras." Proceedings of the Edinburgh Mathematical Society 29, no. 1 (1986): 97–100. http://dx.doi.org/10.1017/s0013091500017454.

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A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified

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8

Farah, Ilijas, and Takeshi Katsura. "Nonseparable Uhf Algebras Ii: Classification." MATHEMATICA SCANDINAVICA 117, no. 1 (2015): 105. http://dx.doi.org/10.7146/math.scand.a-22238.

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For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite ${\rm II}_1$ factors of density character $\kappa$. These estimates are maximal possible. All C*-algebras that we construct have the same Elliott invariant and Cuntz semigroup as the CAR algebra.

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9

KISHIMOTO, A. "UHF FLOWS AND COCYCLES." International Journal of Mathematics 23, no. 01 (2012): 1250018. http://dx.doi.org/10.1142/s0129167x11007598.

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UHF flows are the flows obtained as inductive limits of flows on full matrix algebras. We will revisit universal UHF flows and give an explicit construction of such flows on a UHF algebra Mk∞ for any k and also present a characterization of such flows. Those flows are UHF flows whose cocycle perturbations are almost conjugate to themselves.

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10

Strung, Karen R., and Wilhelm Winter. "UHF-slicing and classification of nuclear C*-algebras." Journal of Topology and Analysis 06, no. 04 (2014): 465–540. http://dx.doi.org/10.1142/s1793525314500198.

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In this paper we show that certain simple locally recursive subhomogeneous (RSH) C*-algebras are tracially approximately interval algebras after tensoring with the universal UHF algebra. This involves a linear algebraic encoding of the structure of the local RSH algebra allowing us to find a path through the algebra which looks like a discrete version of [0, 1] and exhausts most of the algebra. We produce an actual copy of the interval and use properties of C*-algebras tensored with UHF algebras to move the honest interval underneath the discrete version. It follows from our main result that s

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11

MATSUI, TAKU. "MARKOV SEMIGROUPS ON UHF ALGEBRAS." Reviews in Mathematical Physics 05, no. 03 (1993): 587–600. http://dx.doi.org/10.1142/s0129055x93000176.

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We consider a class of Markov semigroups on UHF algebras. We establish the existence of dynamics for long range interactions. Our idea is a non-commutative extension of the argument for classical interacting particle systems. As a by-product we obtain sufficient conditions for unique ergodicity.

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12

Nikolaev, Igor V. "Tate curves and UHF-algebras." Indagationes Mathematicae 27, no. 1 (2016): 383–91. http://dx.doi.org/10.1016/j.indag.2015.11.004.

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13

Stacey, P. J. "A comment on certain p–shift algebras." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, no. 1 (1990): 55–58. http://dx.doi.org/10.1017/s1446788700030238.

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AbstractLet G = ⊕∞i=0Zp, where p is a prime, let s be the shift mapping the i th summand of G to the (i+1) st and let ω be a 2 cocycle on G with values in S1, for which ω (s(g), s(h)) = ω (g, h). If Ω (ej, ek) = Ω (ek, ej) whenever │j - k│ is sufficiently large, where ei is the generator of the i th summand of G, then it is shown that the twisted group C* -algebra C*(G, ω) is isomorphic to the UHF algebra UHF (p∞). An immediate consequence, by results of Bures and Yin, is the existence of infinitely many non-conjugate shifts on UHF (p∞).

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14

Al-Rawashdeh, Ahmed. "On the extension of unitary group isomorphisms of unital UHF-algebras." International Journal of Mathematics 26, no. 08 (2015): 1550061. http://dx.doi.org/10.1142/s0129167x15500615.

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H. Dye showed that an isomorphism between the (discrete) unitary groups in two factors not of type In is implemented by a linear (or a conjugate linear) *-isomorphism of the factors. If φ is an isomorphism between the unitary groups of two unital C*-algebras, it induces a bijective map θφ between the sets of projections. For certain UHF-algebras, we construct an automorphism φ of their unitary group, such that θφ does not preserve the orthogonality of projections. For a large class of unital finite C*-algebras, we show that θφ is always an orthoisomorphism. If φ is a continuous automorphism of

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15

FUTAMURA, HAJIME, NOBUHIRO KATAOKA, and AKITAKA KISHIMOTO. "HOMOGENEITY OF THE PURE STATE SPACE FOR SEPARABLE C*-ALGEBRAS." International Journal of Mathematics 12, no. 07 (2001): 813–45. http://dx.doi.org/10.1142/s0129167x01001015.

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We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the approximately homogeneous C*-algebras and the class of purely infinite C*-algebras which has been recently classified by Kirchberg and Phillips. This extends the known results for UHF algebras and AF algebras by Powers and Bratteli.

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16

EAGLE, CHRISTOPHER J., ILIJAS FARAH, BRADD HART, BORIS KADETS, VLADYSLAV KALASHNYK, and MARTINO LUPINI. "FRAÏSSÉ LIMITS OF C*-ALGEBRAS." Journal of Symbolic Logic 81, no. 2 (2016): 755–73. http://dx.doi.org/10.1017/jsl.2016.14.

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AbstractWe realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1 factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

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17

Matsui, Taku. "A Characterization of Pure Finitely Correlated States." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (1998): 647–61. http://dx.doi.org/10.1142/s0219025798000351.

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18

MATSUI, TAKU. "ON NON-COMMUTATIVE RUELLE TRANSFER OPERATOR." Reviews in Mathematical Physics 13, no. 10 (2001): 1183–201. http://dx.doi.org/10.1142/s0129055x01001034.

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19

OSAKA, HIROYUKI, and TAMOTSU TERUYA. "TOPOLOGICAL STABLE RANK OF INCLUSIONS OF UNITAL C*-ALGEBRAS." International Journal of Mathematics 17, no. 01 (2006): 19–34. http://dx.doi.org/10.1142/s0129167x06003345.

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Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute the topological stable rank of B (= tsr (B)) when A has topological stable rank one. We show that tsr (B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with tsr (D) = 1. When G is a finite group and α is an action of G on UHF, we know that a crossed product algebra UHF ⋊α G has topological stable rank less than or equal to two. These results are affirmative data to a generalization of a question by Blackadar in 1988.

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20

Baker, R. L. "Triangular UHF algebras over arbitrary fields." Proceedings of the American Mathematical Society 123, no. 1 (1995): 67. http://dx.doi.org/10.1090/s0002-9939-1995-1215025-4.

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21

Hudson, Timothy D., Elias G. Katsoulis, and David R. Larson. "Extreme points in triangular UHF algebras." Transactions of the American Mathematical Society 349, no. 8 (1997): 3391–400. http://dx.doi.org/10.1090/s0002-9947-97-01882-5.

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22

Farah, Ilijas, and Takeshi Katsura. "Nonseparable UHF algebras I: Dixmier's problem." Advances in Mathematics 225, no. 3 (2010): 1399–430. http://dx.doi.org/10.1016/j.aim.2010.04.006.

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23

VENTURA, BELISARIO A. "STRONGLY MAXIMAL TRIANGULAR AF ALGEBRAS." International Journal of Mathematics 02, no. 05 (1991): 567–98. http://dx.doi.org/10.1142/s0129167x91000326.

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We consider strongly maximal triangular subalgebras of AF algebras. These are the triangular algebras [Formula: see text] such that [Formula: see text] is dense in the ambient AF algebra. We prove that every isometric isomorphism between two strongly maximal triangular subalgebras of the AF algebra [Formula: see text] factors as the composition of two automorphsims of [Formula: see text], one induced by a homeomorphism of the Gelfand spectrum of the diagonal of [Formula: see text], and the other induced by a cocycle on the groupoid supporting [Formula: see text]. As a consequence we obtain tha

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24

MASUMOTO, SHUHEI. "THE JIANG–SU ALGEBRA AS A FRAÏSSÉ LIMIT." Journal of Symbolic Logic 82, no. 4 (2017): 1541–59. http://dx.doi.org/10.1017/jsl.2016.52.

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AbstractIn this paper, we give a self-contained and quite elementary proof that the class of all dimension drop algebras together with their distinguished faithful traces forms a Fraïssé class with the Jiang–Su algebra as its limit. We also show that the UHF algebras can be realized as Fraïssé limits of classes of C*-algebras of matrix-valued continuous functions on [0,1] with faithful traces.

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25

Sun, Michael. "Strongly outer group actions on UHF algebras." Journal of Topology and Analysis 10, no. 03 (2018): 701–21. http://dx.doi.org/10.1142/s1793525318500231.

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We show that for any countable discrete maximally almost periodic group [Formula: see text] and any UHF algebra [Formula: see text], there exists a strongly outer product type action [Formula: see text] of [Formula: see text] on [Formula: see text]. When [Formula: see text] is also elementary amenable, Matui–Sato have shown that such actions have their tracial Rokhlin property. Consequently, the class of crossed products [Formula: see text] satisfy Elliott’s classification conjecture. We also show the existence of the “Rokhlin” property for countable discrete almost abelian group actions on th

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26

Størmer, Erling. "Separable states and positive maps II." MATHEMATICA SCANDINAVICA 105, no. 2 (2009): 188. http://dx.doi.org/10.7146/math.scand.a-15114.

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Using the natural duality between linear functionals on tensor products of $C^*$-algebras with the trace class operators on a Hilbert space $H$ and linear maps of the $C^*$-algebra into $B(H)$, we give two characterizations of separability, one relating it to abelianness of the definite set of the map, and one on tensor products of nuclear and UHF $C^*$-algebras.

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27

KISHIMOTO, A. "ROHLIN PROPERTY FOR SHIFT AUTOMORPHISMS." Reviews in Mathematical Physics 12, no. 07 (2000): 965–80. http://dx.doi.org/10.1142/s0129055x00000368.

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28

Kutsenko, Anton A. "Classification of Integrodifferential C∗-Algebras." Symmetry 13, no. 10 (2021): 1900. http://dx.doi.org/10.3390/sym13101900.

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The infinite product of matrices with integer entries, known as a modified Glimm–Bratteli symbol n, is a new, sufficiently simple, and very powerful tool for the characterization of approximately finite-dimensional (AF) algebras. This symbol provides a convenient algebraic representation of the Bratteli diagram for AF algebras in the same way as was previously performed by J. Glimm for more simple uniformly hyperfinite (UHF) algebras. We apply this symbol to characterize integrodifferential algebras. The integrodifferential algebra FN,M is the C∗-algebra generated by the following operators ac

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29

Bratteli, Ola, Erling Størmer, Akitaka Kishimoto, and Mikael Rørdam. "The crossed product of a UHF algebra by a shift." Ergodic Theory and Dynamical Systems 13, no. 4 (1993): 615–26. http://dx.doi.org/10.1017/s0143385700007574.

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AbstractWe prove that the crossed product of the CAR algebra M2∞ by the shift is an inductive limit of homogeneous algebras over the circle with fibres full matrix algebras. As a consequence the crossed product has real rank zero, and where is the Cuntz algebra of order 2.

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30

Amini, Massoud, George A. Elliott, and Nasser Golestani. "The Category of Bratteli Diagrams." Canadian Journal of Mathematics 67, no. 5 (2015): 990–1023. http://dx.doi.org/10.4153/cjm-2015-001-8.

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AbstractA category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of AF algebras (and at the same time, of Glimm’s classification of UHF algebras). It is shown that the three approaches to classification of AF algebras, namely, through Bratteli diagrams, K-theory, and a certain natural abstract classifying category, ar

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31

Gardella, Eusebio, and Martino Lupini. "Actions of rigid groups on UHF-algebras." Journal of Functional Analysis 275, no. 2 (2018): 381–421. http://dx.doi.org/10.1016/j.jfa.2017.12.005.

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32

Marcoux, Laurent W., and Yuanhang Zhang. "On Specht's Theorem in UHF C⁎-algebras." Journal of Functional Analysis 280, no. 1 (2021): 108778. http://dx.doi.org/10.1016/j.jfa.2020.108778.

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33

Gardella, Eusebio, and Martino Lupini. "Nonclassifiability of UHF $L^p$-operator algebras." Proceedings of the American Mathematical Society 144, no. 5 (2015): 2081–91. http://dx.doi.org/10.1090/proc/12859.

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34

Kodaka, Kazunori. "Projections inducing automorphisms of stable UHF-algebras." Glasgow Mathematical Journal 41, no. 3 (1999): 345–54. http://dx.doi.org/10.1017/s0017089599000336.

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35

Handelman, David. "Imitation product-type actions on UHF algebras." Journal of Algebra 99, no. 1 (1986): 1–21. http://dx.doi.org/10.1016/0021-8693(86)90050-5.

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36

Lin, Huaxin. "Homomorphisms From C(X) Into C*-Algebras." Canadian Journal of Mathematics 49, no. 5 (1997): 963–1009. http://dx.doi.org/10.4153/cjm-1997-050-9.

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AbstractLet A be a simple C*-algebra with real rank zero, stable rank one and weakly unperforated K0(A) of countable rank. We show that a monomorphism Φ: C(S2) → A can be approximated pointwise by homomorphisms from C(S2) into A with finite dimensional range if and only if certain index vanishes. In particular,we show that every homomorphism ϕ from C(S2) into a UHF-algebra can be approximated pointwise by homomorphisms from C(S2) into the UHF-algebra with finite dimensional range.As an application, we show that if A is a simple C*-algebra of real rank zero and is an inductive limit of matrices

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37

Rørdam, Mikael. "On the structure of simple C∗-algebras tensored with a UHF-algebra." Journal of Functional Analysis 100, no. 1 (1991): 1–17. http://dx.doi.org/10.1016/0022-1236(91)90098-p.

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38

Herman, Richard H., and Adrian Ocneanu. "Spectral analysis for automorphisms of UHF C∗-algebras." Journal of Functional Analysis 66, no. 1 (1986): 1–10. http://dx.doi.org/10.1016/0022-1236(86)90076-5.

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39

Matui, Hiroki, and Yasuhiko Sato. "Decomposition rank of UHF-absorbing $\mathrm{C}^{*}$ -algebras." Duke Mathematical Journal 163, no. 14 (2014): 2687–708. http://dx.doi.org/10.1215/00127094-2826908.

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40

Ramsey, Christopher. "Automorphisms and Dilation Theory of Triangular UHF Algebras." Integral Equations and Operator Theory 77, no. 1 (2013): 89–105. http://dx.doi.org/10.1007/s00020-013-2037-5.

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41

Kishimoto, Akitaka, Narutaka Ozawa, and Shôichirô Sakai. "Homogeneity of the Pure State Space of a Separable C*-Algebra." Canadian Mathematical Bulletin 46, no. 3 (2003): 365–72. http://dx.doi.org/10.4153/cmb-2003-038-3.

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AbstractWe prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algbras some 30 years ago.

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42

HIRSHBERG, ILAN, and WILHELM WINTER. "PERMUTATIONS OF STRONGLY SELF-ABSORBING C*-ALGEBRAS." International Journal of Mathematics 19, no. 09 (2008): 1137–45. http://dx.doi.org/10.1142/s0129167x08005011.

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Let G be a finite group acting on {1,…,n}. For any C*-algebra [Formula: see text], this defines an action α of G on [Formula: see text]. We show that if [Formula: see text] tensorially absorbs a UHF algebra of infinite type, the Jiang–Su algebra, or is approximately divisible, then [Formula: see text] has the corresponding property as well.

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43

Rørdam, Mikael. "On the structure of simple C∗-algebras tensored with a UHF-algebra, II." Journal of Functional Analysis 107, no. 2 (1992): 255–69. http://dx.doi.org/10.1016/0022-1236(92)90106-s.

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44

Peters, J. R., Y. T. Poon, and B. H. Wagner. "Analytic Taf Algebras." Canadian Journal of Mathematics 45, no. 5 (1993): 1009–31. http://dx.doi.org/10.4153/cjm-1993-056-0.

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AbstractA strongly maximal triangular AF algebra which is defined by a realvalued cocycle is said to be analytic. Formulas for generic cocycles are given separately for both the integer-valued case and the real-valued coboundary case, and also for certain nest algebras. In the case of an integer-valued cocycle, there is an associated partial homeomorphismof the maximal ideal space of the diagonal. If the partial homeomorphism extends to a homeomorphism, then the algebra embeds in a crossed product. This occurs for a large class of subalgebras of UHF algebras, but an example shows that this doe

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45

KATAYAMA, Yoshikazu. "Remarks on the fixed point algebras of product type actions on UHF-algebras." Journal of the Mathematical Society of Japan 38, no. 2 (1986): 275–84. http://dx.doi.org/10.2969/jmsj/03820275.

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46

Kishimoto, Akitaka. "The Rohlin Property for Shifts on UHF Algebras and Automorphisms of Cuntz Algebras." Journal of Functional Analysis 140, no. 1 (1996): 100–123. http://dx.doi.org/10.1006/jfan.1996.0100.

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47

Park, Chun-Gil. "The Bundle Structure of Noncommutative Tori over $UHF$-Algebras." Bulletin of the Belgian Mathematical Society - Simon Stevin 10, no. 3 (2003): 321–28. http://dx.doi.org/10.36045/bbms/1063372339.

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48

Thomsen, Klaus. "Ground States for Generalized Gauge Actions on UHF Algebras." Communications in Mathematical Physics 386, no. 1 (2021): 57–85. http://dx.doi.org/10.1007/s00220-021-04075-1.

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49

P., Nathanial. "Crossed products of UHF algebras by some amenable groups." Hokkaido Mathematical Journal 29, no. 1 (2000): 201–11. http://dx.doi.org/10.14492/hokmj/1350912964.

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50

Baker, R. L. "On the Classification of p-Adic UHF Banach Algebras." p-Adic Numbers, Ultrametric Analysis and Applications 10, no. 3 (2018): 166–78. http://dx.doi.org/10.1134/s2070046618030020.

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