Relevant bibliographies by topics / Poisson algebras

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Poisson algebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Poisson algebras"

1

Bavula, V. V. "The generalized Weyl Poisson algebras and their Poisson simplicity criterion." Letters in Mathematical Physics 110, no. 1 (2019): 105–19. http://dx.doi.org/10.1007/s11005-019-01214-7.

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Abstract A new large class of Poisson algebras, the class of generalized Weyl Poisson algebras, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras, and an explicit description of the Poisson centre is obtained. Many examples are considered (e.g. the classical polynomial Poisson algebra in 2n variables is a generalized Weyl Poisson algebra).
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Ait Ben Haddou, Malika, Saïd Benayadi, and Said Boulmane. "Malcev–Poisson–Jordan algebras." Journal of Algebra and Its Applications 15, no. 09 (2016): 1650159. http://dx.doi.org/10.1142/s0219498816501590.

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Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to classify the Jordan structure ∘ on the underlying vector space of [Formula: see text] such that [Formula: see text] is an MPJ-algebra (∘ is called an MPJ-structure on Malcev algebra [Formula: see text]. In this paper we explicitly give all MPJ-s
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LI, HAISHENG. "VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS." Communications in Contemporary Mathematics 06, no. 01 (2004): 61–110. http://dx.doi.org/10.1142/s0219199704001264.

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This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it is proved that the associated graded vector space of a filtered vertex algebra is naturally a vertex Poisson algebra. For any vertex algebra V, a general construction and a classification of good filtrati
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Safronov, Pavel. "Braces and Poisson additivity." Compositio Mathematica 154, no. 8 (2018): 1698–745. http://dx.doi.org/10.1112/s0010437x18007212.

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We relate the brace construction introduced by Calaque and Willwacher to an additivity functor. That is, we construct a functor from brace algebras associated to an operad${\mathcal{O}}$to associative algebras in the category of homotopy${\mathcal{O}}$-algebras. As an example, we identify the category of$\mathbb{P}_{n+1}$-algebras with the category of associative algebras in$\mathbb{P}_{n}$-algebras. We also show that under this identification there is an equivalence of two definitions of derived coisotropic structures in the literature.
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Changjian, Fu, and Peng Lian'gang. "Hall algebras as Poisson algebras." SCIENTIA SINICA Mathematica 48, no. 11 (2018): 1673. http://dx.doi.org/10.1360/n012017-00268.

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Loose, Frank. "Symplectic algebras and poisson algebras." Communications in Algebra 21, no. 7 (1993): 2395–416. http://dx.doi.org/10.1080/00927879308824682.

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Chtioui, T., S. Mabrouk, and A. Makhlouf. "Hom–Jordan–Malcev–Poisson algebras." Ukrains’kyi Matematychnyi Zhurnal 74, no. 11 (2022): 1571–82. http://dx.doi.org/10.37863/umzh.v74i11.6360.

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UDC 512.5 We provide and study a Hom-type generalization of Jordan–Malcev–Poisson algebras called Hom–Jordan–Malcev–Poisson algebras. We show that they are closed under twisting by suitable self-maps and give a characterization of admissible Hom–Jordan–Malcev–Poisson algebras. In addition, we introduce the notion of pseudo-Euclidian Hom–Jordan–Malcev–Poisson algebras and describe its T * -extension. Finally, we generalize the notion of Lie–Jordan–Poisson triple system to the Hom setting and establish its relationships with Hom–Jordan–Malcev–Poisson algebras.
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OKASSA, EUGÈNE. "ON LIE–RINEHART–JACOBI ALGEBRAS." Journal of Algebra and Its Applications 07, no. 06 (2008): 749–72. http://dx.doi.org/10.1142/s0219498808003107.

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We show that Jacobi algebras (Poisson algebras respectively) can be defined only as Lie–Rinehart–Jacobi algebras (as Lie–Rinehart–Poisson algebras respectively). Also we show that contact manifolds, locally conformal symplectic manifolds (symplectic manifolds respectively) can be defined only as symplectic Lie–Rinehart–Jacobi algebras (only as symplectic Lie–Rinehart–Poisson algebras respectively). We define symplectic Lie algebroids.
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Hu, Xianguo. "Universal enveloping Hom-algebras of regular Hom-Poisson algebras." AIMS Mathematics 7, no. 4 (2022): 5712–27. http://dx.doi.org/10.3934/math.2022316.

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<abstract><p>In this paper, we introduce universal enveloping Hom-algebras of Hom-Poisson algebras. Some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras are discussed. Furthermore, in the involutive case, it is proved that the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra $ A $ is equivalent to the category of involutive Hom-associative modules over its universal enveloping Hom-algebra $ U_{eh}(A) $.</p></abstract>
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Kolesnikov, P. S. "Universal enveloping Poisson conformal algebras." International Journal of Algebra and Computation 30, no. 05 (2020): 1015–34. http://dx.doi.org/10.1142/s0218196720500289.

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Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.
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Dissertations / Theses on the topic "Poisson algebras"

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Al-Shujary, Ahmed. "Kähler-Poisson Algebras." Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-150620.

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The focus of this thesis is to introduce the concept of Kähler-Poisson algebras as analogues of algebras of smooth functions on Kähler manifolds. We first give here a review of the geometry of Kähler manifolds and Lie-Rinehart algebras. After that we give the definition and basic properties of Kähler-Poisson algebras. It is then shown that the Kähler type condition has consequences that allow for an identification of geometric objects in the algebra which share several properties with their classical counterparts. Furthermore, we introduce a concept of morphism between Kähler-Poisson algebras
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El, Hadrami Mohamed Lemine Ould 1962. "Poisson algebras and convexity." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290675.

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In this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu.
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Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.

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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu
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Lecoutre, César. "Polynomial Poisson algebras : Gel'fand-Kirillov problem and Poisson spectra." Thesis, University of Kent, 2014. https://kar.kent.ac.uk/47941/.

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We study the fields of fractions and the Poisson spectra of polynomial Poisson algebras. First we investigate a Poisson birational equivalence problem for polynomial Poisson algebras over a field of arbitrary characteristic. Namely, the quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is isomorphic to the field of fractions of a Poisson affine space, i.e. a polynomial algebra such that the Poisson bracket of two generators is equal to their product (up to a scalar). We answer positively the quadratic Poisson Gel'fand-Kirillov problem for a la
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Zwicknagl, Sebastian. "Equivariant Poisson algebras and their deformations /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1280144671&sid=2&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.<br>Typescript. Includes vita and abstract. "In this dissertation I investigate Poisson structures on symmetric and exterior algebras of modules over complex reductive Lie algebras. I use the results to study the braided symmetric and exterior algebras"--P. 1. Includes bibliographical references (leaves 150-152). Also available for download via the World Wide Web; free to University of Oregon users.
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Martino, Maurizio. "Symplectic reflection algebras and Poisson geometry." Thesis, University of Glasgow, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.426614.

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Walker, Lachlan Duncan. "Deformed Poisson W-algebras of type A." Thesis, University of Aberdeen, 2018. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=239477.

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For the algebraic group SLl+1(C) we describe a system of positive roots associated to conjugacy classes in its Weyl group Sl+1. Using this we explicitly describe the algebra of regular functions on certain transverse slices to conjugacy classes in SLl+1(C) as a polynomial algebra of invariants. These may be viewed as an algebraic group analogue of certain parabolic invariants that generate the W-algebra in type A found by Brundan and Kleshchev.
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Damianou, Pantelis Andrea. "Nonlinear Poisson brackets." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184704.

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A hierarchy of vector fields (master symmetries) and homogeneous nonlinear Poisson structures associated with the Toda lattice are constructed and the various connections between them are investigated. Among their properties: new brackets are generated from old ones by using Lie-derivatives in the direction of certain vector fields; the infinite sequences obtained consist of compatible Poisson brackets in which the constants of motion for the Toda lattice are in involution. The vector fields in the construction are unique up to addition of a Hamiltonian vector field. Similarly the Poisson brac
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Casati, Matteo. "Multidimensional Poisson Vertex Algebras and Poisson cohomology of Hamiltonian structures of hydrodynamic type." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4853.

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The Poisson brackets of hydrodynamic type, also called Dubrovin-Novikov brackets, constitute the Hamiltonian structure of a broad class of evolutionary PDEs, that are ubiquitous in the theory of Integrable Systems, ranging from Hopf equation to the principal hierarchy of a Frobenius manifold. They can be regarded as an analogue of the classical Poisson brackets, defined on an infinite dimensional space of maps Σ → M between two manifolds. Our main problem is the study of Poisson-Lichnerowicz cohomology of such space when dim Σ > 1. We introduce the notion of multidimensional Poisson Vertex Al
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Cruz, Ines Maria Bravo de Faria. "The local structure of Poisson manifolds." Thesis, University of Warwick, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309896.

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Books on the topic "Poisson algebras"

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K, Viswanath, ed. Poisson algebras and Poisson manifolds. Longman Scientific & Technical, 1988.

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Laurent-Gengoux, Camille. Poisson Structures. Springer Berlin Heidelberg, 2013.

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V, Karasev M., Shishkova Maria, and American Mathematical Society, eds. Quantum algebras and Poisson geometry in mathematical physics. American Mathematical Society, 2005.

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Rieffel, Marc A. Deformation quantization for actions of Rd̳. American Mathematical Society, 1993.

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Scholma, J. K. A Lie algebraic study of some integrable systems associated with root systems. Centrum voor Wiskunde en Informatica, 1993.

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Dokshevich, A. I. Reshenii͡a︡ v konechnom vide uravneniĭ Ėĭlera-Puassona. Nauk. dumka, 1992.

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1963-, Shapiro Michael, and Vainshtein Alek 1958-, eds. Cluster algebra and Poisson geometry. American Mathematical Society, 2010.

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Molchanov, Ilya S. Statistics of the Boolean model for practitioners and mathematicians. Wiley, 1997.

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Cluster Algebra Structures on Poisson Nilpotent Algebras. American Mathematical Society, 2024.

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Vanhaecke, Pol, Camille Laurent-Gengoux, and Anne Pichereau. Poisson Structures. Springer, 2014.

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Book chapters on the topic "Poisson algebras"

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Adler, Mark, Pierre Moerbeke, and Pol Vanhaecke. "Poisson Manifolds." In Algebraic Integrability, Painlevé Geometry and Lie Algebras. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05650-9_3.

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Martı́n, Antonio J. Calderón, and Diouf Mame Cheikh. "Strongly Split Poisson Algebras." In Non-Associative and Non-Commutative Algebra and Operator Theory. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32902-4_11.

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Rubtsov, Vladimir, and Radek Suchánek. "Lectures on Poisson Algebras." In Groups, Invariants, Integrals, and Mathematical Physics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25666-0_2.

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Martín, Antonio J. Calderón, Boubacar Dieme, and Francisco J. Navarro Izquierdo. "Poisson Algebras and Graphs." In Recent Advances in Pure and Applied Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41321-7_9.

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Adler, Mark, Pierre Moerbeke, and Pol Vanhaecke. "Integrable Systems on Poisson Manifolds." In Algebraic Integrability, Painlevé Geometry and Lie Algebras. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05650-9_4.

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Liu, Guilai, and Chengming Bai. "New Splittings of Operations of Poisson Algebras and Transposed Poisson Algebras and Related Algebraic Structures." In Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-39334-1_2.

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Korogodski, Leonid, and Yan Soibelman. "Poisson Lie groups." In Algebras of Functions on Quantum Groups: Part I. American Mathematical Society, 1998. http://dx.doi.org/10.1090/surv/056/02.

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Benayadi, Saïd. "Construction of Symplectic Quadratic Lie Algebras from Poisson Algebras." In Springer Proceedings in Mathematics & Statistics. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55361-5_8.

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Petrogradsky, Victor. "Identities in Group Rings, Enveloping Algebras and Poisson Algebras." In Springer INdAM Series. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63111-6_17.

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Błaszak, Maciej. "Deformation Theory of Classical Poisson Algebras." In Quantum versus Classical Mechanics and Integrability Problems. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18379-0_6.

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Conference papers on the topic "Poisson algebras"

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Yan, Zhiguo, Tingkun Sun, and Guolin Hu. "New Extended Iterative Algorithms for Solving Stochastic Coupled Algebraic Riccati Equation with Poisson Jump Intensity." In 2024 IEEE 13th Data Driven Control and Learning Systems Conference (DDCLS). IEEE, 2024. http://dx.doi.org/10.1109/ddcls61622.2024.10606760.

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Grabowski, Janusz, and Norbert Poncin. "On quantum and classical Poisson algebras." In Geometry and Topology of Manifolds. Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc76-0-15.

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Damianou, P. A., H. Sabourin, P. Vanhaecke, Rui Loja Fernandes, and Roger Picken. "Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures." In GEOMETRY AND PHYSICS: XVI International Fall Workshop. AIP, 2008. http://dx.doi.org/10.1063/1.2958166.

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Oevel, Walter, and Klaus Strack. "The Yang-Baxter equation and a systematic search for Poisson brackets on associative algebras." In the 1991 international symposium. ACM Press, 1991. http://dx.doi.org/10.1145/120694.120728.

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Codyer, Stephen R., Mehdi Raessi, and Gaurav Khanna. "Using Graphics Processing Units to Accelerate Numerical Simulations of Interfacial Incompressible Flows." In ASME 2012 Fluids Engineering Division Summer Meeting collocated with the ASME 2012 Heat Transfer Summer Conference and the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/fedsm2012-72176.

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We present a GPU accelerated numerical solver for incompressible, immiscible, two-phase fluid flows. This leads to a significant simulation speed-up and thus, the capability to have finer grid sizes and/or more accurate convergence criteria. We solve the Navier-Stokes equations, which include the surface tension force, by using a two-step projection method requiring the iterative solution to a pressure Poisson problem at each time step. However, running a serial linear algebra solver on a CPU to solve the pressure Poisson problem can take 50–99.9% of the total simulation time. To remove this b
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Boffo, Eugenia, and Peter Schupp. "Dual gravity with $R$ flux from graded Poisson algebra." In Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity". Sissa Medialab, 2020. http://dx.doi.org/10.22323/1.376.0140.

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NOUMI, MASATOSHI, and YASUHIKO YAMADA. "BIRATIONAL WEYL GROUP ACTION ARISING FROM A NILPOTENT POISSON ALGEBRA." In Proceedings of the Nagoya 1999 International Workshop. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810199_0010.

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Lopez, Oscar, Daniel Dunlavy, and Richard Lehoucq. "Zero-Truncated Poisson Regression for Multiway Count Data." In Proposed for presentation at the Conference on Random Matrix Theory and Numerical Linear Algebra held June 20-24, 2022 in Seattle, WA. US DOE, 2022. http://dx.doi.org/10.2172/2003556.

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NARA, T., and S. ANDO. "ALGEBRAIC SOLUTION FOR THE INVERSE SOURCE PROBLEM OF THE POISSON EQUATION." In Proceedings of the International Conference on Inverse Problems. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704924_0025.

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Mathur, Sanjay R., and Jayathi Y. Murthy. "A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations." In ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33410.

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Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the
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Reports on the topic "Poisson algebras"

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Yanovski, Alexander. Compatible Poisson Tensors Related to Bundles of Lie Algebras. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-307-319.

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Yanovski, Alexander B. Poisson-Nijenhuis Structure for Generalized Zakharov-Shabat System in Pole Gauge on the Lie Algebra $\mathfrak{sl}(3,\mathbb{C})$. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-342-353.

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