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Relevant bibliographies by topics / Noncommutative algebras

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Academic literature on the topic 'Noncommutative algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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Journal articles on the topic "Noncommutative algebras"

1

Arutyunov, A. A. "Derivation Algebra in Noncommutative Group Algebras." Proceedings of the Steklov Institute of Mathematics 308, no. 1 (January 2020): 22–34. http://dx.doi.org/10.1134/s0081543820010022.

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Zhou, Chaoyuan. "Acyclic Complexes and Graded Algebras." Mathematics 11, no. 14 (July 19, 2023): 3167. http://dx.doi.org/10.3390/math11143167.

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We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated graded free modules is totally acyclic, and we want to generalize such properties to noncommutative N-graded Noetherian algebra. By generalizing the conclusions about commutative rings and combining what we already know about noncommutative graded algebras, we identify a class of noncommutative graded algebras with the property that every minimal

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Abel, Mati, and Krzysztof Jarosz. "Noncommutative uniform algebras." Studia Mathematica 162, no. 3 (2004): 213–18. http://dx.doi.org/10.4064/sm162-3-2.

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Xu, Ping. "Noncommutative Poisson Algebras." American Journal of Mathematics 116, no. 1 (February 1994): 101. http://dx.doi.org/10.2307/2374983.

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Roh, Jaiok, and Ick-Soon Chang. "Approximate Derivations with the Radical Ranges of Noncommutative Banach Algebras." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/594075.

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We consider the derivations on noncommutative Banach algebras, and we will first study the conditions for a derivation on noncommutative Banach algebra. Then, we examine the stability of functional inequalities with a derivation. Finally, we take the derivations with the radical ranges on noncommutative Banach algebras.

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Ercolessi, Elisa, Giovanni Landi, and Paulo Teotonio-Sobrinho. "Noncommutative Lattices and the Algebras of Their Continuous Functions." Reviews in Mathematical Physics 10, no. 04 (May 1998): 439–66. http://dx.doi.org/10.1142/s0129055x98000148.

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Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for their use in quantum physics. Posets are truly noncommutative spaces, or noncommutative lattices, since they can be realized as structure spaces of noncommutative C*-algebras. These noncommutative algebras

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Ferreira, Vitor O., Jairo Z. Gonçalves, and Javier Sánchez. "Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras." International Journal of Algebra and Computation 25, no. 06 (September 2015): 1075–106. http://dx.doi.org/10.1142/s0218196715500319.

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For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring 𝔇(L) constructed by Lichtman. If U(L) is an Ore domain, 𝔇(L) coincides with its ring of fractions. It is well known that the principal involution of L, x ↦ -x, can be extended to an involution of U(L), and Cimpric proved that this involution can be extended to one on 𝔇(L). For a large class of noncommutative Lie algebras L over a field of characteristic zero, we show that 𝔇(L) contains noncommutative free algebras generated by symmetric elements with respect to (the extension of) the pr

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Liang, Shi-Dong, and Matthew J. Lake. "An Introduction to Noncommutative Physics." Physics 5, no. 2 (April 18, 2023): 436–60. http://dx.doi.org/10.3390/physics5020031.

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Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics in a range of areas, including classical physics, condensed matter systems, statistical mechanics, and quantum mechanics, and we present some important examples of noncommutative algebras, including the classical Poisson brackets, the Heisenberg algebra, Lie and Clifford alge

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Mahanta, Snigdhayan. "Noncommutative stable homotopy and stable infinity categories." Journal of Topology and Analysis 07, no. 01 (December 2, 2014): 135–65. http://dx.doi.org/10.1142/s1793525315500077.

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The noncommutative stable homotopy category NSH is a triangulated category that is the universal receptacle for triangulated homology theories on separable C*-algebras. We show that the triangulated category NSH is topological as defined by Schwede using the formalism of (stable) infinity categories. More precisely, we construct a stable presentable infinity category of noncommutative spectra and show that NSHop sits inside its homotopy category as a full triangulated subcategory, from which the above result can be deduced. We also introduce a presentable infinity category of noncommutative po

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LETZTER, EDWARD S. "NONCOMMUTATIVE IMAGES OF COMMUTATIVE SPECTRA." Journal of Algebra and Its Applications 07, no. 05 (October 2008): 535–52. http://dx.doi.org/10.1142/s0219498808002941.

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We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially "sewn together" to form Spec R. In particular, we construct a bimodule-determined functor Mod Z → Mod R, for a suitable commutative noetherian ring Z, from which there follows a finite-to-one, continuous surjection Spec Z → Spec R. Algebras satisfying the given axiomatic framework include PI algebras finitely generated over fields, noetherian PI algebras, envelopin

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Dissertations / Theses on the topic "Noncommutative algebras"

1

Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.

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Hartman, Gregory Neil. "Graphs and Noncommutative Koszul Algebras." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/27156.

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A new connection between combinatorics and noncommutative algebra is established by relating a certain class of directed graphs to noncommutative Koszul algebras. The directed graphs in this class are called full graphs and are defined by a set of criteria on the edges. The structural properties of full graphs are studied as they relate to the edge criteria. A method is introduced for generating a Koszul algebra Lambda from a full graph G. The properties of Lambda are examined as they relate to the structure of G, with special attention being given to the construction of a projective resoluti

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Schoenecker, Kevin J. "An infinite family of anticommutative algebras with a cubic form." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1187185559.

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Russell, Ewan. "Prime ideals in quantum algebras." Thesis, University of Edinburgh, 2009. http://hdl.handle.net/1842/3450.

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The central objects of study in this thesis are quantized coordinate algebras. These algebras originated in the 1980s in the work of Drinfeld and Jumbo and are noncommutative analogues of coordinate rings of algebraic varieties. The organic nature by which these algebras arose is of great interest to algebraists. In particular, investigating ring theoretic properties of these noncommutative algebras in comparison to the properties already known about their classical (commutative) counterparts proves to be a fruitful process. The prime spectrum of an algebra has always been seen as an important

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Phan, Christopher Lee 1980. "Koszul and generalized Koszul properties for noncommutative graded algebras." Thesis, University of Oregon, 2009. http://hdl.handle.net/1794/10367.

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xi, 95 p. : ill. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.<br>We investigate some homological properties of graded algebras. If A is an R -algebra, then E (A) := Ext A ( R, R ) is an R-algebra under the cup product and is called the Yoneda algebra. (In most cases, we assume R is a field.) A well-known and widely-studied condition on E(A) is the Koszul property. We study a class of deformations of Koszul algebras that arises from the study of equivariant cohomology and algebraic groups and show that

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Meyer, Jonas R. "Noncommutative Hardy algebras, multipliers, and quotients." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/712.

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The principal objects of study in this thesis are the noncommutative Hardy algebras introduced by Muhly and Solel in 2004, also called simply ``Hardy algebras,'' and their quotients by ultraweakly closed ideals. The Hardy algebras form a class of nonselfadjoint dual operator algebras that generalize the classical Hardy algebra, the noncommutative analytic Toeplitz algebras introduced by Popescu in 1991, and other classes of operator algebras studied in the literature. It is known that a quotient of a noncommutative analytic Toeplitz algebra by a weakly closed ideal can be represented completel

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Uhl, Christine. "Quantum Drinfeld Hecke Algebras." Thesis, University of North Texas, 2016. https://digital.library.unt.edu/ark:/67531/metadc862764/.

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Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex reflection groups acting in arbitrary dimension. We also classify quantum Drinfeld Hecke algebras i

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Zhao, Xiangui. "Groebner-Shirshov bases in some noncommutative algebras." London Mathematical Society, 2014. http://hdl.handle.net/1993/24315.

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Groebner-Shirshov bases, introduced independently by Shirshov in 1962 and Buchberger in 1965, are powerful computational tools in mathematics, science, engineering, and computer science. This thesis focuses on the theories, algorithms, and applications of Groebner-Shirshov bases for two classes of noncommutative algebras: differential difference algebras and skew solvable polynomial rings. This thesis consists of three manuscripts (Chapters 2--4), an introductory chapter (Chapter 1) and a concluding chapter (Chapter 5). In Chapter 1, we introduce the background and the goals of the thesi

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Oblomkov, Alexei. "Double affine Hecke algebras and noncommutative geometry." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/31165.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.<br>Includes bibliographical references (p. 93-96).<br>In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the center Z of H(t, 1), and H(t, 1)e is a Cohen-Macaulay eH(t, 1)e-module with the property H(t, 1) = EndeH(t,tl)(H(t, 1)e). This implies the classification of the finite

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Gohm, Rolf. "Noncommutative stationary processes /." Berlin [u.a.] : Springer, 2004. http://www.loc.gov/catdir/enhancements/fy0813/2004103932-d.html.

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Books on the topic "Noncommutative algebras"

1

Farb, Benson. Noncommutative algebra. New York: Springer-Verlag, 1993.

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Marubayashi, Hidetoshi. Prime Divisors and Noncommutative Valuation Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Khalkhali, Masoud, and Guoliang Yu. Perspectives on noncommutative geometry. Providence, R.I: American Mathematical Society, 2011.

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4

Silva, Ana Cannas da. Geometric models for noncommutative algebras. Providence, R.I: American Mathematical Society, 1999.

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5

Rosenberg, Alex. Noncommutative algebraic geometry and representations of quantized algebras. Dordrecht: Kluwer Academic Publishers, 1995.

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Cuculescu, I. Noncommutative probability. Dordrecht: Kluwer Academic Publishers, 1994.

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Rosenberg, Alexander L. Noncommutative Algebraic Geometry and Representations of Quantized Algebras. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2.

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Diep, Do Ngoc. Methods of noncommutative geometry for group C*-algebras. Boca Raton: Chapman & Hall/CRC, 2000.

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9

Bonfiglioli, Andrea. Topics in noncommutative algebra: The theorem of Campbell, Baker, Hausdorff and Dynkin. Heidelberg: Springer, 2012.

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Doran, Robert S., and Richard V. Kadison, eds. Operator Algebras, Quantization, and Noncommutative Geometry. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/conm/365.

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Book chapters on the topic "Noncommutative algebras"

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Cuculescu, I., and A. G. Oprea. "Jordan Algebras." In Noncommutative Probability, 293–315. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8374-9_7.

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Arzumanian, Victor, and Suren Grigorian. "Noncommutative Uniform Algebras." In Linear Operators in Function Spaces, 101–9. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7250-8_5.

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Cuculescu, I., and A. G. Oprea. "Probability on von Neumann Algebras." In Noncommutative Probability, 53–94. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8374-9_2.

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Rosenberg, Alexander L. "Noncommutative Affine Schemes." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 1–47. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_1.

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Rosenberg, Alexander L. "Noncommutative Local Algebra." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 110–41. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_3.

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Rosenberg, Alexander L. "Noncommutative Projective Spectrum." In Noncommutative Algebraic Geometry and Representations of Quantized Algebras, 276–305. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8430-2_7.

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Aschieri, Paolo. "Quantum Groups, Quantum Lie Algebras, and Twists." In Noncommutative Spacetimes, 111–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89793-4_7.

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Bratteli, Ola. "Noncommutative vectorfields." In Derivations, Dissipations and Group Actions on C*-algebras, 34–240. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0098820.

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Gracia-Bondía, José M., Joseph C. Várilly, and Héctor Figueroa. "Kreimer-Connes-Moscovici Algebras." In Elements of Noncommutative Geometry, 597–640. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0005-5_14.

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Várilly, Joseph C. "The Interface of Noncommutative Geometry and Physics." In Clifford Algebras, 227–42. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_15.

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Conference papers on the topic "Noncommutative algebras"

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VÁRILLY, JOSEPH C. "HOPF ALGEBRAS IN NONCOMMUTATIVE GEOMETRY." In Proceedings of the Summer School. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705068_0001.

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Schauenburg, P. "Weak Hopf algebras and quantum groupoids." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-12.

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Khalkhali, M., and B. Rangipour. "Cyclic cohomology of (extended) Hopf algebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-5.

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Gomez, X., and S. Majid. "Relating quantum and braided Lie algebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-6.

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Szymański, Wojciech. "Quantum lens spaces and principal actions on graph C*-algebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-18.

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MORI, IZURU. "NONCOMMUTATIVE PROJECTIVE SCHEMES AND POINT SCHEMES." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0014.

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Majewski, Władysław A., and Marcin Marciniak. "On the structure of positive maps between matrix algebras." In Noncommutative Harmonic Analysis with Applications to Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-18.

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Wakui, Michihisa. "The coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras." In Noncommutative Geometry and Quantum Groups. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc61-0-20.

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LONGO, ROBERTO. "OPERATOR ALGEBRAS AND NONCOMMUTATIVE GEOMETRIC ASPECTS IN CONFORMAL FIELD THEORY." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0008.

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Fernández, David, and Luis Álvarez–cónsul. "Noncommutative bi-symplectic $\mathbb{N}Q$-algebras of weight 1." In The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (Madrid, Spain). American Institute of Mathematical Sciences, 2015. http://dx.doi.org/10.3934/proc.2015.0019.

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