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Journal articles on the topic 'Algebraic Structures in Physics'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Jones, Robert Murray. "Algebraic Structures of Quantum Physics." Open Journal of Philosophy 11, no. 03 (2021): 355–57. http://dx.doi.org/10.4236/ojpp.2021.113024.

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2

Duplij, Steven. "Arity Shape of Polyadic Algebraic Structures." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (2019): 3–56. http://dx.doi.org/10.15407/mag15.01.003.

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3

Freed, Daniel S. "Higher algebraic structures and quantization." Communications in Mathematical Physics 159, no. 2 (1994): 343–98. http://dx.doi.org/10.1007/bf02102643.

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4

Tanasa, Adrian. "Algebraic structures in quantum gravity." Classical and Quantum Gravity 27, no. 9 (2010): 095008. http://dx.doi.org/10.1088/0264-9381/27/9/095008.

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5

Doikou, A., and K. Sfetsos. "Contractions of quantum algebraic structures." Fortschritte der Physik 58, no. 7-9 (2010): 879–82. http://dx.doi.org/10.1002/prop.201000032.

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6

Duplij, Steven. "Polyadization of Algebraic Structures." Symmetry 14, no. 9 (2022): 1782. http://dx.doi.org/10.3390/sym14091782.

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A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented as block diagonal matrices (resulting in the Wedderburn decomposition), general forms of polyadic structures are given by block-shift matrices. We combine these forms to get a general shape of semisimple nonderived polyadic structures (“double” decomposition of two kinds). We then introduce the polyadization concept (a “polyadic constructor”), according to which one can construct a nonderived polyadic algebraic structure of any arity from a given binary struct

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7

Kreimer, D. "Algebraic Structures in local QFT." Nuclear Physics B - Proceedings Supplements 205-206 (August 2010): 122–28. http://dx.doi.org/10.1016/j.nuclphysbps.2010.08.030.

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8

KERNER, RICHARD. "TERNARY AND NON-ASSOCIATIVE STRUCTURES." International Journal of Geometric Methods in Modern Physics 05, no. 08 (2008): 1265–94. http://dx.doi.org/10.1142/s0219887808003326.

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We discuss ternary algebraic structures appearing in various domains of theoretical and mathematical physics. Some of them are associative, and some are not. Their interesting and curious properties can be exploited in future applications to enlarged and generalized field theoretical models in the years to come. Many ideas presented here have been developed and clarified in countless discussions with Michel Dubois-Violette.

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9

Chernega, Iryna, Mariia Martsinkiv, Taras Vasylyshyn, and Andriy Zagorodnyuk. "Applications of Supersymmetric Polynomials in Statistical Quantum Physics." Quantum Reports 5, no. 4 (2023): 683–97. http://dx.doi.org/10.3390/quantum5040043.

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We propose a correspondence between the partition functions of ideal gases consisting of both bosons and fermions and the algebraic bases of supersymmetric polynomials on the Banach space of absolutely summable two-sided sequences ℓ1(Z0). Such an approach allows us to interpret some of the combinatorial identities for supersymmetric polynomials from a physical point of view. We consider a relation of equivalence for ℓ1(Z0), induced by the supersymmetric polynomials, and the semi-ring algebraic structures on the quotient set with respect to this relation. The quotient set is a natural model for

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10

Cederwall, Martin. "Algebraic Structures in Extended Geometry." Physics of Particles and Nuclei 49, no. 5 (2018): 873–78. http://dx.doi.org/10.1134/s1063779618050155.

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11

Kulish, P. P., and E. K. Sklyanin. "Algebraic structures related to reflection equations." Journal of Physics A: Mathematical and General 25, no. 22 (1992): 5963–75. http://dx.doi.org/10.1088/0305-4470/25/22/022.

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12

Kramer, P. "Algebraic structures for 1D quasiperiodic systems." Journal of Physics A: Mathematical and General 26, no. 2 (1993): 213–28. http://dx.doi.org/10.1088/0305-4470/26/2/010.

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13

Hammad, M. M., H. E. Shetawy, Ayman A. Aly, and S. B. Doma. "Nuclear supersymmetry and dual algebraic structures." Physica Scripta 94, no. 10 (2019): 105207. http://dx.doi.org/10.1088/1402-4896/ab2442.

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14

Bhadula, Rakesh Chandra. "Investigation of Representation Theory for Algebraic and Geometric Applications." Mathematical Statistician and Engineering Applications 70, no. 1 (2021): 580–86. http://dx.doi.org/10.17762/msea.v70i1.2511.

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Understanding the algebraic and geometric structures that form in diverse mathematical areas depends heavily on the study of representation theory. The significance and uses of representation theory in both algebra and geometry are briefly discussed in this abstract.The primary goal of representation theory is to understand how linear transformations on vector spaces can represent abstract algebraic objects like groups, rings, and algebras. Representation theory offers a strong framework to analyse and interact with these structures using the methods and tools of linear algebra by linking alge

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15

HEYDARI, HOSHANG. "ALGEBRAIC STRUCTURES OF MULTIPARTITE QUANTUM SYSTEMS." International Journal of Quantum Information 09, no. 01 (2011): 555–61. http://dx.doi.org/10.1142/s0219749911005515.

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We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically well-defined manner.

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16

Iğde, Elif, and Koray Yılmaz. "Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes." Symmetry 15, no. 9 (2023): 1646. http://dx.doi.org/10.3390/sym15091646.

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The study of algebraic structures endowed with the concept of symmetry is made possible by the link between Lie algebras and symmetric monoidal categories. This relationship between Lie algebras and symmetric monoidal categories is useful and has resulted in many areas, including algebraic topology, representation theory, and quantum physics. In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing li

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17

Kruis, J., T. Koudelka, and T. Krejcˇí. "Multi-Physics Analyses of Selected Civil Engineering Concrete Structures." Communications in Computational Physics 12, no. 3 (2012): 885–918. http://dx.doi.org/10.4208/cicp.031110.080711s.

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AbstractThis paper summarizes suitable material models for creep and damage of concrete which are coupled with heat and moisture transfer. The fully coupled approach or the staggered coupling is assumed. Governing equations are spatially dis-cretized by the finite element method and the temporal discretization is done by the generalized trapezoidal method. Systems of non-linear algebraic equations are solved by the Newton method. Development of an efficient and extensible computer code based on the C++ programming language is described. Finally, successful analyses of two real engineering prob

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18

Santini, P. M. "The algebraic structures underlying integrability." Inverse Problems 6, no. 1 (1990): 99–114. http://dx.doi.org/10.1088/0266-5611/6/1/010.

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19

Santini, P. M. "The algebraic structures underlying integrability." Inverse Problems 6, no. 3 (1990): 479. http://dx.doi.org/10.1088/0266-5611/6/3/516.

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20

Gustavsson, Andreas. "Algebraic structures on parallel M2 branes." Nuclear Physics B 811, no. 1-2 (2009): 66–76. http://dx.doi.org/10.1016/j.nuclphysb.2008.11.014.

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21

Toyota, N. "On algebraic structures of topological gravity." Physics Letters B 282, no. 3-4 (1992): 314–20. http://dx.doi.org/10.1016/0370-2693(92)90645-k.

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22

Cirilo-Lombardo, Diego Julio. "Algebraic Structures, Physics and Geometry from a Unified Field Theoretical Framework." International Journal of Theoretical Physics 54, no. 10 (2015): 3713–27. http://dx.doi.org/10.1007/s10773-015-2609-z.

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23

Popentiu, Fl. "Network Reliability and Algebraic Structures." Microelectronics Reliability 32, no. 5 (1992): 745. http://dx.doi.org/10.1016/0026-2714(92)90638-2.

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24

Gangopadhyay, Sunandan. "Lie algebraic noncommuting structures from reparametrization symmetry." Journal of Mathematical Physics 48, no. 5 (2007): 052302. http://dx.doi.org/10.1063/1.2723551.

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25

Ansari, Moin A. "Higher-Order Derivations and Their Applications in Algebraic Structures." International Journal of Analysis and Applications 23 (July 16, 2025): 168. https://doi.org/10.28924/2291-8639-23-2025-168.

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We introduce and develop the theory of higher-order derivations on associative algebras, extending the classical notion by defining n-th order derivations that satisfy generalized Leibniz rules involving n + 1 elements. Fundamental properties of these higher-order derivations are established, and explicit examples are provided in polynomial and matrix algebras. We demonstrate that higher-order derivations correspond to elements in the Hochschild cohomology groups HHn(C,C) and show that they define infinitesimal deformations of algebras of order n. Applications are discussed in differential alg

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26

Piattelli-Palmarini, Massimo, and Giuseppe Vitiello. "Linguistics and Some Aspects of Its Underlying Dynamics." Biolinguistics 9 (December 8, 2015): 096–115. http://dx.doi.org/10.5964/bioling.9033.

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In recent years, central components of a new approach to linguistics, the Minimalist Program, have come closer to physics. In this paper, an interesting and productive isomorphism is established between minimalist structure, algebraic structures, and many-body field theory opening new avenues of inquiry on the dynamics underlying some central aspects of linguistics. Features such as the unconstrained nature of recursive Merge, the difference between pronounced and un-pronounced copies of elements in a sentence, and the Fibonacci sequence in the syntactic derivation of sentence structures, are

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27

Cioroianu, Eugen-Mihăiţă, and Cornelia Vizman. "A linear algebraic setting for Jacobi structures." Journal of Geometry and Physics 159 (January 2021): 103904. http://dx.doi.org/10.1016/j.geomphys.2020.103904.

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28

Lv, Quanjin, Xinghao Peng, Yuqing Wu, and Jiaying Zhang. "Algebraic and Topological Structures of Complex Numbers." Journal of Physics: Conference Series 2012, no. 1 (2021): 012071. http://dx.doi.org/10.1088/1742-6596/2012/1/012071.

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29

Ujino, Hideaki, Miki Wadati, and Kazuhiro Hikami. "The Quantum Calogero-Moser Model: Algebraic Structures." Journal of the Physical Society of Japan 62, no. 9 (1993): 3035–43. http://dx.doi.org/10.1143/jpsj.62.3035.

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30

Alkinani, Amnah A., and Ahmad M. Alghamdi. "Algebraic Structures on Smooth Vector Fields." Symmetry 15, no. 12 (2023): 2150. http://dx.doi.org/10.3390/sym15122150.

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The aim of this work is to investigate some algebraic structures of objects which are defined and related to a manifold. Consider L to be a smooth manifold and Γ∞(TL) to be the module of smooth vector fields over the ring of smooth functions C∞(L). We prove that the module Γ∞(TL) is projective and finitely generated, but it is not semisimple. Therefore, it has a proper socle and nonzero Jacobson radical. Furthermore, we prove that this module is reflexive by showing that it is isomorphic to its bidual. Additionally, we investigate the structure of the Lie algebra of smooth vector fields. We gi

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31

Rajchel-Mieldzioć, Grzegorz, Kamil Korzekwa, Zbigniew Puchała, and Karol Życzkowski. "Algebraic and geometric structures inside the Birkhoff polytope." Journal of Mathematical Physics 63, no. 1 (2022): 012202. http://dx.doi.org/10.1063/5.0046581.

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32

Cardoso, Pedro G. S., Ernesto P. Borges, Thierry C. P. Lobão, and Suani T. R. Pinho. "Nondistributive algebraic structures derived from nonextensive statistical mechanics." Journal of Mathematical Physics 49, no. 9 (2008): 093509. http://dx.doi.org/10.1063/1.2982233.

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33

Harrelson, Eric, Alexander A. Voronov, and J. Javier Zúñiga. "Open-Closed Moduli Spaces and Related Algebraic Structures." Letters in Mathematical Physics 94, no. 1 (2010): 1–26. http://dx.doi.org/10.1007/s11005-010-0418-0.

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34

Kaushal Rana. "Homological Algebra and Its Application: A Descriptive Study." Integrated Journal for Research in Arts and Humanities 2, no. 1 (2022): 29–35. http://dx.doi.org/10.55544/ijrah.2.1.47.

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Algebra has been used to define and answer issues in almost every field of mathematics, science, and engineering. Homological algebra depends largely on computable algebraic invariants to categorise diverse mathematical structures, such as topological, geometrical, arithmetical, and algebraic (up to certain equivalences). String theory and quantum theory, in particular, have shown it to be of crucial importance in addressing difficult physics questions. Geometric, topological and algebraic algebraic techniques to the study of homology are to be introduced in this research. Homology theory in a

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35

Figueroa-O’Farrill, José. "Lie algebraic Carroll/Galilei duality." Journal of Mathematical Physics 64, no. 1 (2023): 013503. http://dx.doi.org/10.1063/5.0132661.

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We characterize Lie groups with bi-invariant bargmannian, galilean, or carrollian structures. Localizing at the identity, we show that Lie algebras with ad-invariant bargmannian, carrollian, or galilean structures are actually determined by the same data: a metric Lie algebra with a skew-symmetric derivation. This is the same data defining a one-dimensional double extension of the metric Lie algebra and, indeed, bargmannian Lie algebras coincide with such double extensions, containing carrollian Lie algebras as an ideal and projecting to galilean Lie algebras. This sets up a canonical correspo

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36

MORENO, GIOVANNI. "ON FAMILIES IN DIFFERENTIAL GEOMETRY." International Journal of Geometric Methods in Modern Physics 10, no. 09 (2013): 1350042. http://dx.doi.org/10.1142/s0219887813500424.

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Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows one to work without introducing ad hoc spaces, by using the language of differential calculus over commutative algebras. An advantage of such an approach, based on the notion of sliceable structures on cylinders, is that the fundamental theorems of standard calculus are straightforwardly generalized to the context of families. As an example of that, we prov

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37

Van Hoang Dinh. "Introduction to Algebraic Deformation Theory and The Case of k-Linear Categories." Journal of Technical Education Science 19, SI03 (2024): 72–79. http://dx.doi.org/10.54644/jte.2024.1575.

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Deformation theory is a branch of mathematics which studies how mathematical objects, such as algebraic varieties, schemes, algebras, or categories, can be deformed “continuously” depending on a space of parameter while preserving certain algebraic or geometric structures. Algebraic deformation theory, which was pioneered by Murray Gerstenhaber in 1960s-1970s, established its role as a cornerstone in modern mathematics and theoretical physics. This theory provides a powerful framework for understanding the subtle variations and deformations of mathematical and physical objects depending on a p

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38

Kaushal, Rana. "Homological Algebra and Its Application: A Descriptive Study." Integrated Journal for Research in Arts and Humanities 2, no. 1 (2022): 29–35. https://doi.org/10.55544/ijrah.2.1.47.

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Algebra has been used to define and answer issues in almost every field of mathematics, science, and engineering. Homological algebra depends largely on computable algebraic invariants to categorise diverse mathematical structures, such as topological, geometrical, arithmetical, and algebraic (up to certain equivalences). String theory and quantum theory, in particular, have shown it to be of crucial importance in addressing difficult physics questions. Geometric, topological and algebraic algebraic techniques to the study of homology are to be introduced in this research. Homology theory in a

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39

Artemovych, Orest, Alexander Balinsky, Denis Blackmore, and Anatolij Prykarpatski. "Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky–Novikov Type Symmetry Algebras and Related Hamiltonian Operators." Symmetry 10, no. 11 (2018): 601. http://dx.doi.org/10.3390/sym10110601.

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The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysis on the adjoint space to toroidal loop Lie algebras is employed to construct new reduced pre-Lie algebraic structures in which the corresponding Hamiltonian operators exist and generate integrable dynamical systems. It is also shown that the Balinsky–Novikov type algebraic structures, obtained as a Hamiltonicity condition, are derivations on the Lie alg

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40

MARMO, G., G. SCOLARICI, A. SIMONI, and F. VENTRIGLIA. "ALTERNATIVE ALGEBRAIC STRUCTURES FROM BI-HAMILTONIAN QUANTUM SYSTEMS." International Journal of Geometric Methods in Modern Physics 02, no. 05 (2005): 919–37. http://dx.doi.org/10.1142/s0219887805000831.

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We discuss the alternative algebraic structures on the manifold of quantum states arising from the alternative Hermitian structures associated with the quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of the deformations of the associative product on the space of observables.

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41

Karassiov, V. P. "New Lie-algebraic structures in nonlinear problems of quantum optics and laser physics." Journal of Soviet Laser Research 13, no. 3 (1992): 188–95. http://dx.doi.org/10.1007/bf01121107.

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42

Kaptsov, O. V. "Algebraic and geometric structures of analytic partial differential equations." Theoretical and Mathematical Physics 189, no. 2 (2016): 1592–608. http://dx.doi.org/10.1134/s0040577916110052.

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43

Zeitlin, Anton M. "String field theory-inspired algebraic structures in gauge theories." Journal of Mathematical Physics 50, no. 6 (2009): 063501. http://dx.doi.org/10.1063/1.3142964.

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44

Avan, Jean, and Antal Jevicki. "Algebraic structures and eigenstates for integrable collective field theories." Communications in Mathematical Physics 150, no. 1 (1992): 149–66. http://dx.doi.org/10.1007/bf02096570.

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45

Sen, Ashoke, and Barton Zwiebach. "Background independent algebraic structures in closed string field theory." Communications in Mathematical Physics 177, no. 2 (1996): 305–26. http://dx.doi.org/10.1007/bf02101895.

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46

Cariñena, José F., Janusz Grabowski, and Giuseppe Marmo. "Contractions: Nijenhuis and Saletan tensors for general algebraic structures." Journal of Physics A: Mathematical and General 34, no. 18 (2001): 3769–89. http://dx.doi.org/10.1088/0305-4470/34/18/306.

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47

Richter, Wolf-Dieter. "Three-Complex Numbers and Related Algebraic Structures." Symmetry 13, no. 2 (2021): 342. http://dx.doi.org/10.3390/sym13020342.

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Three-complex numbers are introduced for using a geometric vector product in the three-dimensional Euclidean vector space R3 and proving its equivalence with a spherical coordinate product. Based upon the definitions of the geometric power and geometric exponential functions, some Euler-type trigonometric representations of three-complex numbers are derived. Further, a general l23−complex algebraic structure together with its matrix, polynomial and variable basis vector representations are considered. Then, the classes of lp3-complex numbers are introduced. As an application, Euler-type formul

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48

LÉANDRE, RÉMI. "STOCHASTIC PROCESSES ON CLASSIFYING SPACES AND STRING STRUCTURES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 03 (2004): 361–81. http://dx.doi.org/10.1142/s0219025704001700.

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49

Bai, Chenyu, and Yixuan Chen. "Uncovering Patterns Beneath the Surface: A Glimpse into the Applications of Algebraic Topology." Journal of Contemporary Educational Research 7, no. 12 (2023): 282–89. http://dx.doi.org/10.26689/jcer.v7i12.5823.

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This paper explores the significant impact of algebraic topology on diverse real-world applications. Starting with an introduction to the historical development and essence of algebraic topology, it delves into its applications in neuroscience, physics, biology, engineering, data analysis, and Geographic Information Systems (GIS). Remarkable applications incorporate the analysis of neural networks, quantum mechanics, materials science, and disaster management, showcasing its boundless significance. Despite computational challenges, this study outlines prospects, emphasizing the requirement for

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50

Hatip, Ahmed. "Symbolic 4-Plithogenic Rings and 5-Plithogenic Rings." Symmetry 15, no. 8 (2023): 1588. http://dx.doi.org/10.3390/sym15081588.

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Symbolic n-plithogenic algebraic structures are considered as symmetric generalizations of classical algebraic structures because they have n + 1 symmetric components. This paper is dedicated to generalizing symbolic 3-plithogenic rings by defining symbolic 4-plithogenic rings and 5-plithogenic rings; these new classes of n-symbolic plithogenic algebraic structures will be defined for the first time, and their algebraic substructures will be studied. AH structures are considered to be a sign of the presence of symmetry within these types of ring, as they consist of several parts that are simil

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