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Relevant bibliographies by topics / Algebra of differential operators

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Academic literature on the topic 'Algebra of differential operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Algebra of differential operators"

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SÁNCHEZ, OMAR LEÓN, and RAHIM MOOSA. "THE MODEL COMPANION OF DIFFERENTIAL FIELDS WITH FREE OPERATORS." Journal of Symbolic Logic 81, no. 2 (2016): 493–509. http://dx.doi.org/10.1017/jsl.2015.76.

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AbstractA model companion is shown to exist for the theory of partial differential fields of characteristic zero equipped with free operators that commute with the derivations. The free operators here are those introduced in [R. Moosa and T. Scanlon, Model theory of fields with free operators in characteristic zero, Journal of Mathematical Logic 14(2), 2014]. The proof relies on a new lifting lemma in differential algebra: a differential version of Hensel’s Lemma for local finite algebras over differentially closed fields.

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Vaysburd, I., and A. Radul. "Differential operators and W-algebra." Physics Letters B 274, no. 3-4 (1992): 317–22. http://dx.doi.org/10.1016/0370-2693(92)91991-h.

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Qiu, Jianjun. "Gröbner–Shirshov bases for commutative algebras with multiple operators and free commutative Rota–Baxter algebras." Asian-European Journal of Mathematics 07, no. 02 (2014): 1450033. http://dx.doi.org/10.1142/s1793557114500338.

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In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner–Shirshov bases and linear bases of free commutative Rota–Baxter algebra, free commutative λ-differential algebra and free commutative λ-differential Rota–Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative Ω-words.

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Gao, Xing, Li Guo, and Markus Rosenkranz. "On rings of differential Rota–Baxter operators." International Journal of Algebra and Computation 28, no. 01 (2018): 1–36. http://dx.doi.org/10.1142/s0218196718500017.

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Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota–Baxter operator. In applying the general framework to univariate polynomials, one is led to the integro–differential analogs of the classical Weyl algebra. These are analyzed in terms of skew polynomial rings and noncommutative Gröbner bases.

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Galkin, Oleg E., and Svetlana Y. Galkina. "On the invertibility of solutions of first order linear homogeneous differential equations in Banach algebras." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 21, no. 4 (2019): 430–42. http://dx.doi.org/10.15507/2079-6900.21.201904.430-442.

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This work is devoted to the study of some properties of linear homogeneous differential equations of the first order in Banach algebras. It is found (for some types of Banach algebras), at what right-hand side of such an equation, from the invertibility of the initial condition it follows the invertibility of its solution at any given time. Associative Banach algebras over the field of real or complex numbers are considered. The right parts of the studied equations have the form [F(t)](x(t)), where {F(t)} is a family of bounded operators on the algebra, continuous with respect to t∈R. The problem is to find all continuous families of bounded operators on algebra, preserving the invertibility of elements from it, for a given Banach algebra. In the proposed article, this problem is solved for only three cases. In the first case, the algebra consists of all square matrices of a given order. For this algebra, it is shown that all continuous families of operators, preserving the invertibility of elements from the algebra at zero must be of the form [F(t)](y)=a(t)⋅y+y⋅b(t), where the families {a(t)} and {b(t)} are also continuous. In the second case, the algebra consists of all continuous functions on the segment. For this case, it is shown that all families of operators, preserving the invertibility of elements from the algebra at any time must be of the form [F(t)](y)=a(t)⋅y, where the family {a(t)} is also continuous. The third case concerns those Banach algebras in which all nonzero elements are invertible. For example, the algebra of complex numbers and the algebra of quaternions have this property. In this case, any continuous families of bounded operators preserves the invertibility of the elements from the algebra at any time. The proposed study is in contact with the research of the foundations of quantum mechanics. The dynamics of quantum observables is described by the Heisenberg equation. The obtained results are an indirect argument in favor of the fact, that the known form of the Heisenberg equation is the only correct one.

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Wood, RMW. "Differential Operators and the Steenrod Algebra." Proceedings of the London Mathematical Society 75, no. 1 (1997): 194–220. http://dx.doi.org/10.1112/s0024611597000324.

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Humi, M. "Perturbation algebra of invariant differential operators." Il Nuovo Cimento B Series 11 91, no. 1 (1986): 115–25. http://dx.doi.org/10.1007/bf02722225.

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Bavula, V. V. "The global dimension of the algebras of polynomial integro-differential operators 𝕀n and the Jacobian algebras 𝔸n". Journal of Algebra and Its Applications 19, № 02 (2019): 2050030. http://dx.doi.org/10.1142/s0219498820500309.

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The aim of the paper is to prove two conjectures from the paper [V. V. Bavula, The algebra of integro-differential operators on a polynomial algebra, J. London Math. Soc. (2) 83 (2011) 517–543, arXiv:math.RA/0912.0723] that the (left and right) global dimension of the algebra [Formula: see text] of polynomial integro-differential operators and the Jacobian algebra [Formula: see text] is equal to [Formula: see text] (over a field of characteristic zero). The algebras [Formula: see text] and [Formula: see text] are neither left nor right Noetherian and [Formula: see text]. Furthermore, they contain infinite direct sums of nonzero left/right ideals and are not domains. An analogue of Hilbert’s Syzygy Theorem is proven for the algebras [Formula: see text], [Formula: see text] and their factor algebras. It is proven that the global dimension of all prime factor algebras of the algebras [Formula: see text] and [Formula: see text] is [Formula: see text] and the weak global dimension of all the factor algebras of [Formula: see text] and [Formula: see text] is [Formula: see text].

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Futorny, Vyacheslav, and João Schwarz. "Holonomic modules for rings of invariant differential operators." International Journal of Algebra and Computation 31, no. 04 (2021): 605–22. http://dx.doi.org/10.1142/s0218196721500296.

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We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals 1.

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Toppan, Francesco, and Mauricio Valenzuela. "Higher-Spin Symmetries and Deformed Schrödinger Algebra in Conformal Mechanics." Advances in Mathematical Physics 2018 (September 2, 2018): 1–10. http://dx.doi.org/10.1155/2018/6263150.

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The dynamical symmetries of 1+1-dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial de Alfaro-Fubini-Furlan, DFF, term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the sl(2)⊕u(1) invariance of the Calogero Conformal Mechanics, an osp2∣2 invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher-spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable.

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Dissertations / Theses on the topic "Algebra of differential operators"

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Moroianu, Sergiu 1973. "Residue functionals on the algebra of adiabatic pseudo-differential operators." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85306.

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Glencross, Alexander Iain. "Invariant differential operators on the representation space of a quiver." Thesis, University of Sheffield, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366103.

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Turner, Simon Charles. "Differential operators on algebraic varieties." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386865.

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Lewis, Benjamin. "Primitive factor rings of p-adic completions of enveloping algebras as arithmetic differential operators." Thesis, Queen Mary, University of London, 2015. http://qmro.qmul.ac.uk/xmlui/handle/123456789/9549.

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We study the -adic completion dD[1] of Berthelot's differential operators of level one on the projective line over a complete discrete valuation ring of mixed characteristic (0; p). The global sections are shown to be isomorphic to a Morita context whose objects are certain fractional ideals of primitive factor rings of the -adic completion of the universal enveloping algebra of sl2(R). We produce a bijection between the coadmissibly primitive ideals of the Arens Michael envelope of a nilpotent finite dimensional Lie algebra and the classical universal enveloping algebra. We make limited progress towards characterizing the primitive ideals of certain a noid enveloping algebras of nilpotent Lie algebras under restrictive conditions on the Lie algebra. We produce an isomorphism between the primitive factor rings of these affinoid enveloping algebras and matrix rings over certain deformations of Berthelot's arithmetic differential operators over the a fine line.

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Dines, Nicoleta, and Bert-Wolfgang Schulze. "Mellin-edge representations of elliptic operators." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2662/.

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We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.

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Baston, Robert J. "The algebraic construction of invariant differential operators." Thesis, University of Oxford, 1985. http://ora.ox.ac.uk/objects/uuid:a7cb5790-7267-47d2-9179-df705405ae08.

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Let G be a complex semisimple Lie Group with parabolic subgroup P, so that G/P is a generalized flag manifold. An algebraic construction of invariant differential operators between sections of homogeneous bundles over such spaces is given and it is shown how this leads to the classification of all such operators. As an example of a process which naturally generates such operators, the algebraic Penrose transform between generalized flag manifolds is given and computed for several cases, extending standard results in Twistor Theory to higher dimensions. It is then shown how to adapt the homogeneous construction to manifolds with a certain class of tangent bundle structure, including conformal manifolds. This leads to a natural definition of invariant differential operators on such manifolds, and an algebraic method for their construction. A curved analogue of the Penrose transform is given.

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Chung, Myungsuk. "Lie derivations on rings of differential operators." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/37457.

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Gover, Ashwin Roderick. "A geometrical construction of conformally invariant differential operators." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329953.

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Herlemont, Basile. "Differential calculus on h-deformed spaces." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0377/document.

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L'anneau $\Diff(n)$ des opérateurs différentiels $\h$-déformés apparaît dans la théorie des algèbres de réduction.Dans cette thèse, nous construisons les anneaux des opérateurs différentiels généralisés sur les espaces vectoriels $\h$-déformés de type $\gl$. Contrairement aux espaces vectoriels $q$-déformés pour lequel l'anneau des opérateurs différentiels est unique \`a isomorphisme pr\`es, l'anneau généralisé des opérateurs différentiels $\h$-déformés $\Diffs(n)$ est indexée par une fonction rationnelle $\sigma$ en $n$ variables, solution d'un syst\`eme d\'eg\'en\'er\'e d'\'equations aux diff\'erences finies. Nous obtenons la solution g\'en\'erale de ce syst\`eme. Nous montrons que le centre de $\Diffs(n)$ est un anneau des polynômes en $n$ variables. Nous construisons un isomorphisme entre des localisations de l'anneau $\Diffs(n)$ et de l’algèbre de Weyl $\text{W}_n$ l’étendue par $n$ indéterminés. Nous présentons des conditions irréductibilité des modules de dimension fini de $\Diffs(n)$. Finalement, nous discutons des difficultés a trouver les constructions analogues pour l'anneau $\Diff(n,N)$ correspondant \`a $N$ copies de $\Diff(n)$
The ring $\Diff(n)$ of $\h$-deformed differential operators appears in the theory of reduction algebras. In this thesis, we construct the rings of generalized differential operators on the $\h$-deformed vector spaces of $\gl$-type. In contrast to the $q$-deformed vector spaces for which the ring of differential operators is unique up to an isomorphism, the general ring of $\h$-deformed differential operators $\Diffs(n)$ is labeled by a rational function $\sigma$ in $n$ variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system. We show that the center of $\Diffs(n)$ is a ring of polynomials in $n$ variables. We construct an isomorphism between certain localizations of $\Diffs(n)$ and the Weyl algebra $\W_n$ extended by $n$ indeterminates. We present some conditions for the irreducibility of the finite dimensional $\Diffs(n)$-modules. Finally, we discuss difficulties for finding analogous constructions for the ring $\Diff(n, N)$ formed by several copies of $\Diff(n)$

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Sharif, H. "Algebraic functions, differentially algebraic power series and Hadamard operations." Thesis, University of Kent, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235336.

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Books on the topic "Algebra of differential operators"

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1922-, Markus L., ed. Elliptic partial differential operators and symplectic algebra. American Mathematical Society, 2003.

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1951-, Stafford J. T., ed. Rings of differential operators on classical rings of invariants. American Mathematical Society, 1989.

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Turner, Simon Charles. Differential operators on algebraic varieties. typescript, 1993.

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1922-, Markus L., ed. Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators. American Mathematical Society, 1999.

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1832489.

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The monograph is devoted to the fundamental aspects of geometric algebra and closely related issues. The category of Clifford algebras is considered as the conjugate category of vector spaces with a quadratic form. Possible constructions in this category and internal algebraic operations of an algebra with a geometric interpretation are studied. An application to the differential geometry of a Euclidean manifold based on a shape tensor is included. We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Clifford algebras into simple components. Spinors are introduced. Methods of matrix representation of the Clifford algebra are studied. It may be of interest to students, postgraduates and specialists in the field of mathematics, physics and cybernetics.

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Musson, Ian M. Invariants under tori of rings of differential operators and related topics. American Mathematical Society, 1998.

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Yakubov, S. Differential-operator equations: Ordinary and partial differential equations. Chapman & Hall/CRC, 2000.

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Spectral theory of linear differential operators and comparison algebras. Cambridge University Press, 1987.

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Krasilʹshchik, I. S. Symmetries and recursion operators for classical and supersymmetric differential equations. Kluwer Academic, 2000.

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Arveson, William, Thomas Branson, and Irving Segal, eds. Quantization, Nonlinear Partial Differential Equations, and Operator Algebra. American Mathematical Society, 1996. http://dx.doi.org/10.1090/pspum/059.

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Book chapters on the topic "Algebra of differential operators"

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Cordes, H. O., and S. H. Doong. "The Laplace comparison algebra of spaces with conical and cylindrical ends." In Pseudo-Differential Operators. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077738.

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Poinsot, Laurent. "Differential (Monoid) Algebra and More." In Algebraic and Algorithmic Aspects of Differential and Integral Operators. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54479-8_8.

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Singh, Anurag K. "A Polynomial Identity via Differential Operators." In Homological and Computational Methods in Commutative Algebra. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61943-9_14.

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Tannenbaum, Allen, and Anthony Yezzi. "Differential Invariants and Curvature Flows in Active Vision." In Operators, Systems and Linear Algebra. Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-09823-2_16.

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Shemyakova, Ekaterina. "Multiple Factorizations of Bivariate Linear Partial Differential Operators." In Computer Algebra in Scientific Computing. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04103-7_26.

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Ruzhansky, Michael, and Ville Turunen. "Algebras." In Pseudo-Differential Operators and Symmetries. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8514-9_5.

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Smith, S. P. "Differential operators on commutative algebras." In Ring Theory. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076323.

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Horozov, Emil. "Dual algebras of differential operators." In The Kowalevski Property. American Mathematical Society, 2002. http://dx.doi.org/10.1090/crmp/032/07.

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Nestruev, Jet. "Differential Operators over Graded Algebras." In Graduate Texts in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45650-4_21.

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Ruzhansky, Michael, and Ville Turunen. "Hopf Algebras." In Pseudo-Differential Operators and Symmetries. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-8514-9_14.

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Conference papers on the topic "Algebra of differential operators"

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Dobrev, Vladimir. "Invariant Differential Operators for the Real Exceptional Lie Algebra $F'_4$." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0233.

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Ndogmo, J. C. "On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra." In APPLIED MATHEMATICS AND COMPUTER SCIENCE: Proceedings of the 1st International Conference on Applied Mathematics and Computer Science. Author(s), 2017. http://dx.doi.org/10.1063/1.4982017.

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Regensburger, Georg. "Symbolic Computation with Integro-Differential Operators." In ISSAC '16: International Symposium on Symbolic and Algebraic Computation. ACM, 2016. http://dx.doi.org/10.1145/2930889.2930942.

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Giesbrecht, Mark, Qiao-Long Huang, and Éric Schost. "Sparse Multiplication of Multivariate Linear Differential Operators." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. ACM, 2021. http://dx.doi.org/10.1145/3452143.3465527.

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Camlibel, Kanat, Luigi Iannelli, Aneel Tanwani, and Stephan Trenn. "Differential-algebraic inclusions with maximal monotone operators." In 2016 IEEE 55th Conference on Decision and Control (CDC). IEEE, 2016. http://dx.doi.org/10.1109/cdc.2016.7798336.

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Hounkonnou, M. N., P. D. Sielenou, Piotr Kielanowski, et al. "An Algebraic Method of Factorization of Ordinary Differential Operators." In XXVIII WORKSHOP ON GEOMETRICAL METHODS IN PHYSICS. AIP, 2009. http://dx.doi.org/10.1063/1.3275580.

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Nabeshima, Katsusuke, Katsuyoshi Ohara, and Shinichi Tajima. "Comprehensive Gröbner Systems in Rings of Differential Operators, Holonomic D-modules and B-functions." In ISSAC '16: International Symposium on Symbolic and Algebraic Computation. ACM, 2016. http://dx.doi.org/10.1145/2930889.2930918.

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Dougherty, Edward R., and Charles R. Giardina. "Image Algebra - Induced Operators And Induced Subalgebras." In 1987 Cambridge Symposium, edited by T. Russell Hsing. SPIE, 1987. http://dx.doi.org/10.1117/12.976515.

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Camargo, Rubens De Figueiredo, Eliana Contharteze Grigoletto, and Edmundo Capelas De Oliveira. "Fractional Differential Operators: Eigenfunctions." In CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2018. http://dx.doi.org/10.5540/03.2018.006.01.0368.

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BOUZAR, CHIKH, and RACHID CHAILI. "ITERATES OF DIFFERENTIAL OPERATORS." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0015.

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Reports on the topic "Algebra of differential operators"

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Bao, Gang, and William W. Symes. Computation of Pseudo-Differential Operators. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada455455.

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Ustunel, A. S. Hypoellipticity of the Stochastic Partial Differential Operators. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada170326.

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Malitsky, N., A. Reshetov, and Y. Yan. ZLIB++: Object-oriented numerical library for differential algebra. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10147641.

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Yan, Yiton T. ZLIB++: Object Oriented Numerical Library for Differential Algebra. Office of Scientific and Technical Information (OSTI), 2003. http://dx.doi.org/10.2172/813295.

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Yan, Y. Applications of differential algebra to single-particle dynamics in storage rings. Office of Scientific and Technical Information (OSTI), 1991. http://dx.doi.org/10.2172/5166998.

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Malitsky, Nikolay. Application of a Differential Algebra approach to a RHIC Helical Dipole. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/1119445.

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Svetlana G. Shasharina. Final report: Efficient and user friendly C++ library for differential algebra. Office of Scientific and Technical Information (OSTI), 1998. http://dx.doi.org/10.2172/761041.

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Berz, M., E. Forest, and J. Irwin. Exact computation of derivatives with differential algebra and applications to beam dynamics. Office of Scientific and Technical Information (OSTI), 1988. http://dx.doi.org/10.2172/7050634.

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Malitsky, N. Application of a Differential Algebra Approach to a RHIC Helical Dipole (12/94). Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/1149789.

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Caspi, S., M. Helm, L. J. Laslett, and V. O. Brady. An approach to 3D magnetic field calculation using numerical and differential algebra methods. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/7252409.

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