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Relevant bibliographies by topics / Quantum superalgebras;topological invariants;three-manifolds

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Journal articles
Dissertations / Theses
Book chapters

Academic literature on the topic 'Quantum superalgebras;topological invariants;three-manifolds'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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Journal articles on the topic "Quantum superalgebras;topological invariants;three-manifolds"

1

Blumen, Sacha C. "Quantum superalgebras at roots of unity and topological invariants of three-manifolds." Bulletin of the Australian Mathematical Society 73, no. 3 (2006): 479. http://dx.doi.org/10.1017/s0004972700035498.

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ZHANG, R. B. "QUANTUM SUPERGROUPS AND TOPOLOGICAL INVARIANTS OF THREE-MANIFOLDS." Reviews in Mathematical Physics 07, no. 05 (1995): 809–31. http://dx.doi.org/10.1142/s0129055x95000311.

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The Reshetikhin-Turaev approach to topological invariants of three-manifolds is generalized to quantum supergroups. A general method for constructing three-manifold invariant is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, Uq(gl(2|1)) at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.

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3

GUILARTE, JUAN MATEOS. "FUSION RULES, TOPOLOGICAL QUANTUM MECHANICS AND THREE-MANIFOLDS." Modern Physics Letters A 08, no. 31 (1993): 3001–10. http://dx.doi.org/10.1142/s021773239300341x.

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Path-integral quantization of Chern-Simons field theory in the Hamiltonian formalism is developed. A derivation of Verlinde algebra in topological quantum mechanics arises and three-manifold invariants are recovered.

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BRODA, BOGUSŁAW. "CHERN–SIMONS APPROACH TO THREE-MANIFOLD INVARIANTS." Modern Physics Letters A 10, no. 06 (1995): 487–93. http://dx.doi.org/10.1142/s0217732395000521.

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A new, formal, noncombinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of nonperturbative topological quantum Chern–Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is shown.

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MILLETT, KENNETH C. "TOPOLOGICAL QUANTUM FIELD THEORY AND INVARIANTS OF SPATIAL GRAPHS." International Journal of Modern Physics B 06, no. 11n12 (1992): 1825–46. http://dx.doi.org/10.1142/s0217979292000888.

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According to Sir Michael Atiyah [At], the study of topological quantum field theory is equivalent to the study of invariant quantities associated to three-dimensional manifolds. Although one has long considered the classical homology and cohomology structures and their extremely successful generalizations, the real subject of the Atiyah assertion is the new invariants proposed by Witten associated to the Jones polynomials of classical knots and links in the three-dimensional sphere. There have been many manifestations described by Reshetikhin & Turaev [Re1&2], Turaev & Viro [TV], L

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6

Karowski, M., and R. Schrader. "State sum invariants of three-manifolds: A combinatorial approach to topological quantum field theories." Journal of Geometry and Physics 11, no. 1-4 (1993): 181–90. http://dx.doi.org/10.1016/0393-0440(93)90052-g.

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7

ZHANG, R. B., and H. C. LEE. "LICKORISH INVARIANT AND QUANTUM OSP(1|2)." Modern Physics Letters A 11, no. 29 (1996): 2397–406. http://dx.doi.org/10.1142/s0217732396002381.

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Lickorish’s method for constructing topological invariants of three-manifolds is generalized to the quantum supergroup setting. An invariant is obtained by applying this method to the Kauffman polynomial arising from the vector representation of U q( osp (1|2)). A transparent proof is also given showing that this invariant is equivalent to the U q( osp (1|2)) invariant obtained in an earlier publication.

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Cui, Shawn X., and Zhenghan Wang. "State sum invariants of three manifolds from spherical multi-fusion categories." Journal of Knot Theory and Its Ramifications 26, no. 14 (2017): 1750104. http://dx.doi.org/10.1142/s0218216517501048.

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We define a family of quantum invariants of closed oriented [Formula: see text]-manifolds using spherical multi-fusion categories (SMFCs). The state sum nature of this invariant leads directly to [Formula: see text]-dimensional topological quantum field theories ([Formula: see text]s), which generalize the Turaev–Viro–Barrett–Westbury ([Formula: see text]) [Formula: see text]s from spherical fusion categories. The invariant is given as a state sum over labeled triangulations, which is mostly parallel to, but richer than the [Formula: see text] approach in that here the labels live not only on

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9

BOI, LUCIANO. "IDEAS OF GEOMETRIZATION, GEOMETRIC INVARIANTS OF LOW-DIMENSIONAL MANIFOLDS, AND TOPOLOGICAL QUANTUM FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 06, no. 05 (2009): 701–57. http://dx.doi.org/10.1142/s0219887809003783.

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The aim of the first part of this paper is to make some reflections on the role of geometrical and topological concepts in the developments of theoretical physics, especially in gauge theory and string theory, and we show the great significance of these concepts for a better understanding of the dynamics of physics. We will claim that physical phenomena essentially emerge from the geometrical and topological structure of space–time. The attempts to solve one of the central problems in 20th theoretical physics, i.e. how to combine gravity and the other forces into an unitary theoretical explana

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Dissertations / Theses on the topic "Quantum superalgebras;topological invariants;three-manifolds"

1

Blumen, Sacha Carl. "Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds." University of Sydney. School of Mathematics and Statistics, 2005. http://hdl.handle.net/2123/715.

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The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudomodular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra Uq(osp(1|2n)) over C is considered with q a primitive Nth root of unity for all integers N &gt = 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U^(N)_q(osp(1|2n)) = U_q(os

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Book chapters on the topic "Quantum superalgebras;topological invariants;three-manifolds"

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"Chapter IV. Three-dimensional topological quantum field theory." In Quantum Invariants of Knots and 3-Manifolds. De Gruyter, 2016. http://dx.doi.org/10.1515/9783110435221-006.

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"Chapter IV. Three-dimensional topological quantum field theory." In Quantum Invariants of Knots and 3-Manifolds. De Gruyter, 1994. http://dx.doi.org/10.1515/9783110883275-005.

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